Answer:
Final answer will be the choice which matches best with expression
[tex]\frac{x^2+4x-1}{x\left(x+2\right)}[/tex] or
[tex]\frac{x^2+4x-1}{x^2+2x}[/tex]
Step-by-step explanation:
Given expression is:
[tex]\frac{\left(x+5\right)}{\left(x+2\right)}-\frac{\left(x+1\right)}{\left(x^2+2x\right)}[/tex]
We begin by factoring denominators:
[tex]=\frac{\left(x+5\right)}{\left(x+2\right)}-\frac{\left(x+1\right)}{x\left(x+2\right)}[/tex]
Multiply and divide first term by (x) to make denominators equal.
[tex]=\frac{x\left(x+5\right)}{x\left(x+2\right)}-\frac{\left(x+1\right)}{x\left(x+2\right)}[/tex]
Since denominators are equal so we can combine numerators.
[tex]=\frac{x\left(x+5\right)-\left(x+1\right)}{x\left(x+2\right)}[/tex]
Now simplify
[tex]=\frac{x^2+5x-x-1}{x\left(x+2\right)}[/tex]
[tex]=\frac{x^2+4x-1}{x\left(x+2\right)}[/tex]
[tex]=\frac{x^2+4x-1}{x^2+2x}[/tex]
Hence final answer will be the choice which matches best with expression
[tex]\frac{x^2+4x-1}{x\left(x+2\right)}[/tex] or
[tex]\frac{x^2+4x-1}{x^2+2x}[/tex]
