PROBLEM-SOLVING
6 Simplify the following algebraic
a

Ask by Schultz Joseph. in Australia

Jan 20,2025

Question

PROBLEM-SOLVING 6 Simplify the following algebraic a $$ \frac{5}{x+1}+\frac{2}{x+4} $$

UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ \frac{5}{x+1}+\frac{2}{x+4} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{5}{x+1}+\frac{2}{x+4}$$
- step1: Reduce fractions to a common denominator:
  $$\frac{5\left(x+4\right)}{\left(x+1\right)\left(x+4\right)}+\frac{2\left(x+1\right)}{\left(x+4\right)\left(x+1\right)}$$
- step2: Rewrite the expression:
  $$\frac{5\left(x+4\right)}{\left(x+1\right)\left(x+4\right)}+\frac{2\left(x+1\right)}{\left(x+1\right)\left(x+4\right)}$$
- step3: Transform the expression:
  $$\frac{5\left(x+4\right)+2\left(x+1\right)}{\left(x+1\right)\left(x+4\right)}$$
- step4: Multiply the terms:
  $$\frac{5x+20+2\left(x+1\right)}{\left(x+1\right)\left(x+4\right)}$$
- step5: Multiply the terms:
  $$\frac{5x+20+2x+2}{\left(x+1\right)\left(x+4\right)}$$
- step6: Add the terms:
  $$\frac{7x+22}{\left(x+1\right)\left(x+4\right)}$$
- step7: Multiply the terms:
  $$\frac{7x+22}{x^{2}+5x+4}$$
The simplified form of the expression $$ \frac{5}{x+1}+\frac{2}{x+4} $$ is $$ \frac{7x+22}{x^{2}+5x+4} $$.
The simplified form is $$ \frac{7x+22}{x^{2}+5x+4} $$.

PROBLEM-SOLVING
6 Simplify the following algebraic
a

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