Complex fraction made of sums involving rational expressions: Problem…
Simplify.

Ask by Stewart Wood. in the United States

Jan 05,2025

Question

Complex fraction made of sums involving rational expressions: Problem... Simplify. $$ \frac{\frac{5}{v-2}-\frac{1}{v+6}}{\frac{6}{v+6}-\frac{2}{v-2}} $$

UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ \frac{\frac{5}{v-2}-\frac{1}{v+6}}{\frac{6}{v+6}-\frac{2}{v-2}} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{\frac{5}{v-2}-\frac{1}{v+6}}{\frac{6}{v+6}-\frac{2}{v-2}}$$
- step1: Subtract the terms:
  $$\frac{\frac{4v+32}{\left(v-2ight)\left(v+6ight)}}{\frac{6}{v+6}-\frac{2}{v-2}}$$
- step2: Subtract the terms:
  $$\frac{\frac{4v+32}{\left(v-2ight)\left(v+6ight)}}{\frac{4v-24}{\left(v+6ight)\left(v-2ight)}}$$
- step3: Multiply by the reciprocal:
  $$\frac{4v+32}{\left(v-2ight)\left(v+6ight)}	imes \frac{\left(v+6ight)\left(v-2ight)}{4v-24}$$
- step4: Rewrite the expression:
  $$\frac{4\left(v+8ight)}{\left(v-2ight)\left(v+6ight)}	imes \frac{\left(v+6ight)\left(v-2ight)}{4\left(v-6ight)}$$
- step5: Reduce the fraction:
  $$\left(v+8ight)	imes \frac{1}{v-6}$$
- step6: Multiply the terms:
  $$\frac{v+8}{v-6}$$
The simplified form of the complex fraction is $$ \frac{v+8}{v-6} $$.
The simplified form of the complex fraction is $$ \frac{v+8}{v-6} $$.

Complex fraction made of sums involving rational expressions: Problem…
Simplify.

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Complex fraction made of sums involving rational expressions: Problem… Simplify.