Question

algebra 2
name
id:1
multiplying & dividing rational expressions
date
period 7
simplify each expression.

1. $\frac{x-6}{x^{2}-11x+30} div \frac{x-4}{x^{2}+x-30}$
2. $\frac{p+8}{p^{2}+18p+80} div \frac{1}{2p+20}$
3. $\frac{n^{2}+4n-21}{n^{2}-9n+18} div \frac{n+7}{8}$
4. $\frac{x-4}{x-8} cdot \frac{x^{2}-14x+48}{x-4}$
5. $\frac{k-9}{k+10} cdot \frac{k^{2}+7k-30}{4k^{2}-12k}$
6. $\frac{n-10}{8n-80} cdot \frac{10n}{7}$
7. $\frac{10x^{2}-70x}{3x} cdot \frac{5}{10x^{2}-70x}$
8. $\frac{m-2}{m^{2}-3m+2} div \frac{1}{m+8}$

Explanation:

Step1: Factorizar polinomios

$\frac{x-6}{(x-5)(x-6)} \div \frac{x-4}{(x+6)(x-5)}$

Step2: Cambiar a multiplicación inversa

$\frac{x-6}{(x-5)(x-6)} \cdot \frac{(x+6)(x-5)}{x-4}$

Step3: Simplificar términos comunes

$\frac{\cancel{x-6}}{\cancel{(x-5)}\cancel{(x-6)}} \cdot \frac{(x+6)\cancel{(x-5)}}{x-4}$

Step1: Factorizar polinomios

$\frac{p+8}{(p+8)(p+10)} \div \frac{1}{2(p+10)}$

Step2: Cambiar a multiplicación inversa

$\frac{p+8}{(p+8)(p+10)} \cdot \frac{2(p+10)}{1}$

Step3: Simplificar términos comunes

$\frac{\cancel{p+8}}{\cancel{(p+8)}\cancel{(p+10)}} \cdot \frac{2\cancel{(p+10)}}{1}$

Step1: Factorizar polinomios

$\frac{(n+7)(n-3)}{(n-3)(n-6)} \div \frac{n+7}{8}$

Step2: Cambiar a multiplicación inversa

$\frac{(n+7)(n-3)}{(n-3)(n-6)} \cdot \frac{8}{n+7}$

Step3: Simplificar términos comunes

$\frac{\cancel{(n+7)}\cancel{(n-3)}}{\cancel{(n-3)}(n-6)} \cdot \frac{8}{\cancel{n+7}}$

Step1: Factorizar polinomio

$\frac{x-4}{x-8} \cdot \frac{(x-6)(x-8)}{x-4}$

Step2: Simplificar términos comunes

$\frac{\cancel{x-4}}{\cancel{x-8}} \cdot \frac{(x-6)\cancel{(x-8)}}{\cancel{x-4}}$

Answer:

$\frac{x+6}{x-4}$

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