Chapter 11, Problem 45SGR

To determine

To simplify: the given expression.

Answer to Problem 45SGR

Therefore, the simplified expression is $\frac{x^2+8x-65}{x^2+8x+12}$ .

Explanation of Solution

Given: $\frac{x-\frac{35}{x+2}}{x+\frac{42}{x+13}}$

Calculation:

The expression is simplified below.

  $\begin{array}{l}\frac{x-\frac{35}{x+2}}{x+\frac{42}{x+13}}\\ =\frac{\frac{x^2+2x-35}{x+2}}{\frac{x^2+13x+42}{x+13}}\\ =\frac{x^2+2x-35}{x+2}÷\frac{x^2+13x+42}{x+13}\\ =\frac{x^2+2x-35}{x+2}\times \frac{x+13}{x^2+13x+42}\\ =\frac{x^2+8x-65}{x^2+8x+12}\end{array}$

Therefore, the simplified expression is $\frac{x^2+8x-65}{x^2+8x+12}$ .

Conclusion:

Therefore, the simplified expression is $\frac{x^2+8x-65}{x^2+8x+12}$ .