Question

I need help with this​

Answer 1

Answer:

We conclude that:

$\frac{x+2}{x+4}-\frac{x-1}{x+6}=\frac{5x+16}{\left(x+4\right)\left(x+6\right)}$

Step-by-step explanation:

Given the expression

$\frac{x+2}{x+4}-\frac{x-1}{x+6}$

Least Common Multiple of x+4, x+6:  (x+4) (x+6)

Adjusting fractions based on the LCM

$=\frac{\left(x+2\right)\left(x+6\right)}{\left(x+4\right)\left(x+6\right)}-\frac{\left(x-1\right)\left(x+4\right)}{\left(x+6\right)\left(x+4\right)}$

since the denominators are equal, combine the fractions:

$\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

so the expression becomes

$=\frac{\left(x+2\right)\left(x+6\right)-\left(x-1\right)\left(x+4\right)}{\left(x+4\right)\left(x+6\right)}$

$=\frac{x^2+8x+12-\left(x-1\right)\left(x+4\right)}{\left(x+4\right)\left(x+6\right)}$

$=\frac{x^2+8x+12-x^2-3x+4}{\left(x+4\right)\left(x+6\right)}$

simplify

$=\frac{5x+16}{\left(x+4\right)\left(x+6\right)}$

Therefore, we conclude that:

$\frac{x+2}{x+4}-\frac{x-1}{x+6}=\frac{5x+16}{\left(x+4\right)\left(x+6\right)}$