What is 7/(x^2+6x+8)-x/(x+2) ?

The solution to 7/(x^2+6x+8)-x/(x+2) is (7-x^2-4x)/((x+2)(x+4))

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simplify 7/(x^2+6x+8)-x/(x+2)

simplify

\frac{7}{x ^{2} + 6 x + 8} - \frac{x}{x + 2}

\frac{7 - x ^{2} - 4 x}{( x + 2 ) ( x + 4 )}

Solution steps

\frac{7}{x ^{2} + 6 x + 8} - \frac{x}{x + 2}

Least Common Multiplier of

x^{2} + 6 x + 8, x + 2 : (x + 2) (x + 4)

Adjust Fractions based on the LCM

= \frac{7}{( x + 2 ) ( x + 4 )} - \frac{x ( x + 4 )}{( x + 2 ) ( x + 4 )}

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

= \frac{7 - x ( x + 4 )}{( x + 2 ) ( x + 4 )}

Simplify

7 - x (x + 4) : 7 - x^{2} - 4 x

= \frac{7 - x ^{2} - 4 x}{( x + 2 ) ( x + 4 )}

3 + (- 6)

(s + 1) (s + 1)

\frac{7}{24} \times \frac{3}{14} \times \frac{6}{18} \times \frac{8}{3}

\frac{( \frac{5 x ^{4} y ^{2}}{4 x y ^{7}} ) ^{2}}{( \frac{10 x ^{3} y ^{2}}{2 x ^{5} y} )}

- 2 x^{2} - 4 x + 6

What is 7/(x^2+6x+8)-x/(x+2) ?
The solution to 7/(x^2+6x+8)-x/(x+2) is (7-x^2-4x)/((x+2)(x+4))