Divide $$ \frac{x+7}{x-8} \div \frac{x+4}{x^{2}-5 x-24} $$

Question

UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ (x+7)/(x-8) / (x+4)/(x^2-5x-24) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{\frac{\frac{\left(x+7ight)}{\left(x-8ight)}}{\left(x+4ight)}}{\left(x^{2}-5x-24ight)}$$
- step1: Remove the parentheses:
  $$\frac{\frac{\frac{x+7}{x-8}}{x+4}}{x^{2}-5x-24}$$
- step2: Divide the terms:
  $$\frac{\frac{x+7}{\left(x-8ight)\left(x+4ight)}}{x^{2}-5x-24}$$
- step3: Multiply by the reciprocal:
  $$\frac{x+7}{\left(x-8ight)\left(x+4ight)}	imes \frac{1}{x^{2}-5x-24}$$
- step4: Multiply the terms:
  $$\frac{x+7}{\left(x-8ight)\left(x+4ight)\left(x^{2}-5x-24ight)}$$
- step5: Simplify:
  $$\frac{x+7}{\left(x-8ight)^{2}\left(x+4ight)\left(x+3ight)}$$
- step6: Expand the expression:
  $$\frac{x+7}{x^{4}-9x^{3}-36x^{2}+256x+768}$$
The division of $$ \frac{x+7}{x-8} $$ by $$ \frac{x+4}{x^{2}-5x-24} $$ simplifies to $$ \frac{x+7}{x^{4}-9x^{3}-36x^{2}+256x+768} $$.
The expression simplifies to $$ \frac{x+7}{x^{4}-9x^{3}-36x^{2}+256x+768} $$.

Divide \[ \frac{x+7}{x-8} \div \frac{x+4}{x^{2}-5 x-24} \]

Solución de inteligencia artificial de Upstudy

Responder

Solución

preguntas relacionadas

Latest Algebra Questions