QuestionSimplify the expression $\frac{2 x^{2}+11 x+5}{x^{2}-25}$ .

Studdy Solution

STEP 1

Assumptions1. The expression to simplify is $\frac{ x^{}+11 x+5}{x^{}-25}$

STEP 2

We can simplify the expression by factoring the numerator and the denominator.
The numerator factors are obtained by finding two numbers that multiply to $(2*5)=10$ and add to $11$ . Those numbers are $5$ and $2$ .
The denominator is a difference of squares, which can be factored as $(a+b)(a-b)$ where $a$ is $x$ and $b$ is $5$ .

STEP 3

Factor the numerator and the denominator.
The numerator is factored as $(2x+1)(x+5)$ and the denominator as $(x+5)(x-5)$ .
$\frac{2 x^{2}+11 x+5}{x^{2}-25} = \frac{(2x+1)(x+5)}{(x+5)(x-5)}$

STEP 4

Now, we can cancel out the common factors in the numerator and the denominator.
The common factor is $(x+)$ .

STEP 5

Cancel out the common factor $(x+5)$ in the numerator and the denominator.
$\frac{(2x+1)(x+5)}{(x+5)(x-5)} = \frac{2x+1}{x-5}$ The simplified form of the expression $\frac{2 x^{2}+11 x+5}{x^{2}-25}$ is $\frac{2x+1}{x-5}$ .

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