What is x/(x^2+15x+56)-7/(x^2+13x+42) ?

The solution to x/(x^2+15x+56)-7/(x^2+13x+42) is (x-8)/((x+8)(x+6))

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simplify x/(x^2+15x+56)-7/(x^2+13x+42)

simplify

\frac{x}{x ^{2} + 15 x + 56} - \frac{7}{x ^{2} + 13 x + 42}

\frac{x - 8}{( x + 8 ) ( x + 6 )}

Solution steps

\frac{x}{x ^{2} + 15 x + 56} - \frac{7}{x ^{2} + 13 x + 42}

Least Common Multiplier of

x^{2} + 15 x + 56, x^{2} + 13 x + 42 : (x + 7) (x + 8) (x + 6)

Adjust Fractions based on the LCM

= \frac{x ( x + 6 )}{( x + 7 ) ( x + 8 ) ( x + 6 )} - \frac{7 ( x + 8 )}{( x + 7 ) ( x + 8 ) ( x + 6 )}

Apply the fraction rule:

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

= \frac{x ( x + 6 ) - 7 ( x + 8 )}{( x + 7 ) ( x + 8 ) ( x + 6 )}

Simplify

x (x + 6) - 7 (x + 8) : x^{2} - x - 56

= \frac{x ^{2} - x - 56}{( x + 7 ) ( x + 8 ) ( x + 6 )}

Cancel

\frac{x ^{2} - x - 56}{( x + 7 ) ( x + 8 ) ( x + 6 )} : \frac{x - 8}{( x + 8 ) ( x + 6 )}

= \frac{x - 8}{( x + 8 ) ( x + 6 )}

\frac{9 - tan ^{2} ( θ )}{tan ^{2} ( θ ) - 5 tan ( θ ) + 6}

1 6^{2} - x

\frac{( a + b ) ^{3} - ( c + d ) ^{3}}{( a + b ) - ( c + d )}

2 f (x)

(7 a + 10 b + 2 c) - (3 a - c)

What is x/(x^2+15x+56)-7/(x^2+13x+42) ?
The solution to x/(x^2+15x+56)-7/(x^2+13x+42) is (x-8)/((x+8)(x+6))