what is the difference?\n$\frac{x + 5}{x + 2}-\frac{x + 1}{x^{2}+2x}$\n$\frac{x^{2}+4x - 1}{x(x +…

what is the difference?\n$\frac{x + 5}{x + 2}-\frac{x + 1}{x^{2}+2x}$\n$\frac{x^{2}+4x - 1}{x(x + 2)}$\n$\frac{x^{2}+4x + 1}{x(x + 2)}$\n$\frac{4}{-1(x^{2}+x - 2)}$\n$\frac{x^{2}+6x + 1}{x(x + 2)}$

what is the difference?\n$\frac{x + 5}{x + 2}-\frac{x + 1}{x^{2}+2x}$\n$\frac{x^{2}+4x - 1}{x(x + 2)}$\n$\frac{x^{2}+4x + 1}{x(x + 2)}$\n$\frac{4}{-1(x^{2}+x - 2)}$\n$\frac{x^{2}+6x + 1}{x(x + 2)}$

Answer

Explanation:

Step1: Factor the denominator

The denominator of the second - fraction $x^{2}+2x=x(x + 2)$.

Step2: Find a common denominator

The common denominator of $\frac{x + 5}{x + 2}$ and $\frac{x + 1}{x^{2}+2x}$ is $x(x + 2)$. Rewrite $\frac{x + 5}{x + 2}$ as $\frac{(x + 5)\cdot x}{(x + 2)\cdot x}=\frac{x^{2}+5x}{x(x + 2)}$.

Step3: Subtract the fractions

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

Step4: Simplify the numerator

$x^{2}+5x-(x + 1)=x^{2}+5x - x-1=x^{2}+4x - 1$.

Answer:

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