Solved: ?Add Rational Expressions with a Common Denominator In the following exercises

Add: \(\frac{7}{16}+\frac{5}{16}\). Text Transcription: 7/16+5/16

Add: \(\frac{3}{10}+\frac{1}{10}\). Text Transcription: 3/10+1/10

Add: \(\frac{5 x}{2 x+3}+\frac{2}{2 x+3}\). Text Transcription: 5x/2x+3+2/2x+3

Add: \(\frac{x}{x-2}+\frac{1}{x-2}\) . Text Transcription: x/x-2 + 1/x-2

Add: \(\frac{9 x+14}{x+7}+\frac{x^{2}}{x+7}\). Text Transcription: 9x+14/x+7 + x^2/x+7

Add: \(\frac{x^{2}+8 x}{x+5}+\frac{15}{x+5}\). Text Transcription: x^2+8x/x+5 + 15/x+5

Subtract: \(\frac{x^{2}}{x+3}-\frac{9}{x+3}\). Text Transcription: x^2/x+3 - 9/x+3

Subtract: \(\frac{4 x^{2}}{2 x-5}-\frac{25}{2 x-5}\). Text Transcription: 4x^2/2 x-5 - 25/2x-5

Subtract: \(\frac{n^{2}}{n-4}-\frac{n+12}{n-4}\). Text Transcription: n^2/n-4 - n+12/n-4

Subtract: \(\frac{y^{2}}{y-1}-\frac{9 y-8}{y-1}\). Text Transcription: y^2/y-1 - 9y-8/y-1

Subtract: \(\frac{4 x^{2}-11 x+8}{x^{2}-3 x+2}-\frac{3 x^{2}+x-3}{x^{2}-3 x+2}\). Text Transcription: 4x^2-11x+8/x^2-3 x+2 - 3x^2+x-3/x^2-3x+2

Subtract: \(\frac{6 x^{2}-x+20}{x^{2}-81}-\frac{5 x^{2}+11 x-7}{x^{2}-81}\). Text Transcription: 6x^2-x+20/x^2-81 - 5x^2+11x-7/x^2-81

Add: \(\frac{8 x-15}{2 x-5}+\frac{2 x}{5-2 x}\). Text Transcription: 8x-15/2x-5 + 2x/5-2x

Add: \(\frac{6 y^{2}+7 y-10}{4 y-7}+\frac{2 y^{2}+2 y+11}{7-4 y}\). Text Transcription: 6y^2+7y-10/4y-7 + 2y^2+2y+11/7-4y

Subtract: \(\frac{y^{2}-5 y}{y^{2}-4}-\frac{6 y-6}{4-y^{2}}\). Text Transcription: y^2-5y/y{2-4 - 6y-6/4-y^2

Subtract: \(\frac{2 n^{2}+8 n-1}{n^{2}-1}-\frac{n^{2}-7 n-1}{1-n^{2}}\). Text Transcription: 2n^2+8n-1/n^2-1 - n^2-7n-1/1-n^2

Add Rational Expressions with a Common Denominator In the following exercises, add. \(\frac{2}{15}+\frac{7}{15}\) Text Transcription: 2/15 + 7/15

Add Rational Expressions with a Common Denominator In the following exercises, add. \(\frac{4}{21}+\frac{3}{21}\) Text Transcription: 4/21 + 3/21

Add Rational Expressions with a Common Denominator In the following exercises, add. \(\frac{7}{24}+\frac{11}{24}\) Text Transcription: 7/24 + 11/24

Add Rational Expressions with a Common Denominator In the following exercises, add. \(\frac{7}{36}+\frac{13}{36}\) Text Transcription: 7/36 + 13/36

Add Rational Expressions with a Common Denominator In the following exercises, add. \(\frac{3 a}{a-b}+\frac{1}{a-b}\) Text Transcription: 3a/a-b + 1/a-b

Add Rational Expressions with a Common Denominator In the following exercises, add. \(\frac{3 c}{4 c-5}+\frac{5}{4 c-5}\) Text Transcription: 3c/4c-5 + 5/4c-5

Add Rational Expressions with a Common Denominator In the following exercises, add. \(\frac{d}{d+8}+\frac{5}{d+8}\) Text Transcription: d/d+8 + 5/d+8

Add Rational Expressions with a Common Denominator In the following exercises, add. \(\frac{7 m}{2 m+n}+\frac{4}{2 m+n}\) Text Transcription: 7m/2m+n + 4/2m+n

Add Rational Expressions with a Common Denominator In the following exercises, add. \(\frac{p^{2}+10 p}{p+2}+\frac{16}{p+2}\) Text Transcription: p^2+10p/p+2 + 16/p+2

Add Rational Expressions with a Common Denominator In the following exercises, add. \(\frac{q^{2}+12 q}{q+3}+\frac{27}{q+3}\) Text Transcription: q^2+12q/q+3 + 27/q+3

Add Rational Expressions with a Common Denominator In the following exercises, add. \(\frac{2 r^{2}}{2 r-1}+\frac{15 r-8}{2 r-1}\) Text Transcription: 2r^2/2r-1 + 15r-8/2r-1

Add Rational Expressions with a Common Denominator In the following exercises, add. \(\frac{3 s^{2}}{3 s-2}+\frac{13 s-10}{3 s-2}\) Text Transcription: 3s^2/3s-2 + 13s-10/3s-2

Add Rational Expressions with a Common Denominator In the following exercises, add. \(\frac{8 t^{2}}{t+4}+\frac{32 t}{t+4}\) Text Transcription: 8t^2/t+4 + 32t/t+4

Add Rational Expressions with a Common Denominator In the following exercises, add. \(\frac{6 v^{2}}{v+5}+\frac{30 v}{v+5}\) Text Transcription: 6v^2/v+5 + 30v/v+5

Add Rational Expressions with a Common Denominator In the following exercises, add. \(\frac{2 w^{2}}{w^{2}-16}+\frac{8 w}{w^{2}-16}\) Text Transcription: 2w^2/w^2-16 + 8w/w^2-16

Add Rational Expressions with a Common Denominator In the following exercises, add. \(\frac{7 x^{2}}{x^{2}-9}+\frac{21 x}{x^{2}-9}\) Text Transcription: 7x^2/x^2-9 + 21x/x^2-9

Subtract Rational Expressions with a Common Denominator In the following exercises, subtract. \(\frac{y^{2}}{y+8}-\frac{64}{y+8}\) Text Transcription: y^2/y+8 - 64/y+8

Subtract Rational Expressions with a Common Denominator In the following exercises, subtract. \(\frac{z^{2}}{z+2}-\frac{4}{z+2}\) Text Transcription: z^2/z+2 - 4/z+2

Subtract Rational Expressions with a Common Denominator In the following exercises, subtract. \(\frac{9 a^{2}}{3 a-7}-\frac{49}{3 a-7}\) Text Transcription: 9a^2/3a-7 - 49/3a-7

Subtract Rational Expressions with a Common Denominator In the following exercises, subtract. \(\frac{25 b^{2}}{5 b-6}-\frac{36}{5 b-6}\) Text Transcription: 25b^2/5b-6 - 36/5b-6

Subtract Rational Expressions with a Common Denominator In the following exercises, subtract. \(\frac{c^{2}}{c-8}-\frac{6 c+16}{c-8}\) Text Transcription: c^2/c-8 - 6c+16/c-8

Subtract Rational Expressions with a Common Denominator In the following exercises, subtract. \(\frac{d^{2}}{d-9}-\frac{6 d+27}{d-9}\) Text Transcription: d^2/d-9 - 6d+27/d-9

Subtract Rational Expressions with a Common Denominator In the following exercises, subtract. \(\frac{3 m^{2}}{6 m-30}-\frac{21 m-30}{6 m-30}\) Text Transcription: 3m^2/6m-30 - 21m-30/6m-30

Subtract Rational Expressions with a Common Denominator In the following exercises, subtract. \(\frac{2 n^{2}}{4 n-32}-\frac{18 n-16}{4 n-32}\) Text Transcription: 2n^2/4n-32 - 18n-16/4n-32

Subtract Rational Expressions with a Common Denominator In the following exercises, subtract. \(\frac{6 p^{2}+3 p+4}{p^{2}+4 p-5}-\frac{5 p^{2}+p+7}{p^{2}+4 p-5}\) Text Transcription: 6p^2+3p+4/p^2+4p-5 - 5p^2+p+7/p^2+4p-5

Subtract Rational Expressions with a Common Denominator In the following exercises, subtract. \(\frac{5 q^{2}+3 q-9}{q^{2}+6 q+8}-\frac{4 q^{2}+9 q+7}{q^{2}+6 q+8}\) Text Transcription: 5q^2+3q-9/q^2+6q+8 - 4q^2+9q+7/q^2+6q+8

Subtract Rational Expressions with a Common Denominator In the following exercises, subtract. \(\frac{5 r^{2}+7 r-33}{r^{2}-49}-\frac{4 r^{2}+5 r+30}{r^{2}-49}\) Text Transcription: 5r^2+7r-33/r^2-49 - 4r^2+5r+30/r^2-49

Subtract Rational Expressions with a Common Denominator In the following exercises, subtract. \(\frac{7 t^{2}-t-4}{t^{2}-25}-\frac{6 t^{2}+12 t-44}{t^{2}-25}\) Text Transcription: 7t^2-t-4/t^2-25 - 6t^2+12t-44/t^2-25

Add and Subtract Rational Expressions whose Denominators are Opposites In the following exercises, add. \(\frac{10 v}{2 v-1}+\frac{2 v+4}{1-2 v}\) Text Transcription: 10v/2v-1 + 2v+4/1-2v

Add and Subtract Rational Expressions whose Denominators are Opposites In the following exercises, add. \(\frac{20 w}{5 w-2}+\frac{5 w+6}{2-5 w}\) Text Transcription: 20w/5w-2 + 5w+6/2-5w

Add and Subtract Rational Expressions whose Denominators are Opposites In the following exercises, add. \(\frac{10 x^{2}+16 x-7}{8 x-3}+\frac{2 x^{2}+3 x-1}{3-8 x}\) Text Transcription: 10x^2+16x-7/8x-3 + 2x^2+3x-1/3-8x

Add and Subtract Rational Expressions whose Denominators are Opposites In the following exercises, add. \(\frac{6 y^{2}+2 y-11}{3 y-7}+\frac{3 y^{2}-3 y+17}{7-3 y}\) Text Transcription: 6y^2+2y-11/3y-7 + 3y^2-3y+17/7-3y

In the following exercises, subtract. \(\frac{z^{2}+6 z}{z^{2}-25}-\frac{3 z+20}{25-z^{2}}\) Text Transcription: z^2+6z/z^2-25 - 3z+20/25-z^2

In the following exercises, subtract. \(\frac{a^{2}+3 a}{a^{2}-9}-\frac{3 a-27}{9-a^{2}}\) Text Transcription: a^2+3a/a^2-9 - 3a-27/9-a^2

In the following exercises, subtract. \(\frac{2 b^{2}+30 b-13}{b^{2}-49}-\frac{2 b^{2}-5 b-8}{49-b^{2}}\) Text Transcription: 2b^2+30b-13/b^2-49 - 2b^2-5b-8/49-b^2

In the following exercises, subtract. \(\frac{c^{2}+5 c-10}{c^{2}-16}-\frac{c^{2}-8 c-10}{16-c^{2}}\) Text Transcription: c^2+5c-10/c^2-16 - c^2-8c-10/16-c^2

Sarah ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. If r represents Sarah’s speed when she ran, then her running time is modeled by the expression \(\frac{8}{r}\) and her biking time is modeled by the expression \(\frac{24}{r+4}\). Add the rational expressions \(\frac{8}{r}+\frac{24}{r+4}\) to get an expression for the total amount of time Sarah ran and biked. Text Transcription: 8/r 24/r+4 8/r + 24/r+4

If Pete can paint a wall in p hours, then in one hour he can paint \(\frac{1}{p}\) of the wall. It would take Penelope 3 hours longer than Pete to paint the wall, so in one hour she can paint \(\frac{1}{p+3}\) of the wall. Add the rational expressions \(\frac{1}{p}+\frac{1}{p+3}\) to get an expression for the part of the wall Pete and Penelope would paint in one hour if they worked together. Text Transcription: 1/p 1/p+3 1/p + 1/p+3

Writing Exercises Donald thinks that \(\frac{3}{x}+\frac{4}{x}\) is \(\frac{7}{2 x} . Is Donald correct? Explain. Text Transcription: 3/x+4/x 7/2x

Writing Exercises Explain how you find the Least Common Denominator of \(x^{2}+5 x+4\) and \(x^{2}-16\). Text Transcription: x^2+5x+4 x^2-16