Question

Which expression is equivalent to the following complex fraction? X+5/x+2-x+1/x^2+2x

Answer 1

Answer:

Final answer will be the choice which matches best with expression

$\frac{x^2+4x-1}{x\left(x+2\right)}$ or

$\frac{x^2+4x-1}{x^2+2x}$

Step-by-step explanation:

Given expression is:

$\frac{\left(x+5\right)}{\left(x+2\right)}-\frac{\left(x+1\right)}{\left(x^2+2x\right)}$

We begin by factoring denominators:

$=\frac{\left(x+5\right)}{\left(x+2\right)}-\frac{\left(x+1\right)}{x\left(x+2\right)}$

Multiply and divide first term by (x) to make denominators equal.

$=\frac{x\left(x+5\right)}{x\left(x+2\right)}-\frac{\left(x+1\right)}{x\left(x+2\right)}$

Since denominators are equal so we can combine numerators.

$=\frac{x\left(x+5\right)-\left(x+1\right)}{x\left(x+2\right)}$

Now simplify

$=\frac{x^2+5x-x-1}{x\left(x+2\right)}$

$=\frac{x^2+4x-1}{x\left(x+2\right)}$

$=\frac{x^2+4x-1}{x^2+2x}$

Hence final answer will be the choice which matches best with expression

$\frac{x^2+4x-1}{x\left(x+2\right)}$ or

$\frac{x^2+4x-1}{x^2+2x}$