What is 2/(x+3)-1/(x^2+7x+12) ?

The solution to 2/(x+3)-1/(x^2+7x+12) is (2x+7)/((x+3)(x+4))

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simplify 2/(x+3)-1/(x^2+7x+12)

simplify

\frac{2}{x + 3} - \frac{1}{x ^{2} + 7 x + 12}

\frac{2 x + 7}{( x + 3 ) ( x + 4 )}

Solution steps

\frac{2}{x + 3} - \frac{1}{x ^{2} + 7 x + 12}

Least Common Multiplier of

x + 3, x^{2} + 7 x + 12 : (x + 3) (x + 4)

Adjust Fractions based on the LCM

= \frac{2 ( x + 4 )}{( x + 3 ) ( x + 4 )} - \frac{1}{( x + 3 ) ( x + 4 )}

Apply the fraction rule:

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

= \frac{2 ( x + 4 ) - 1}{( x + 3 ) ( x + 4 )}

Simplify

2 (x + 4) - 1 : 2 x + 7

= \frac{2 x + 7}{( x + 3 ) ( x + 4 )}

\frac{3}{4} \div \frac{5}{7}

(sec^{2} (x) + csc^{2} (x)) - (tan^{2} (x) + cot^{2} (x))

\frac{8 6 mn + 6 8 mn}{2 2 mn}

(6 x - x^{2})^{2}

What is 2/(x+3)-1/(x^2+7x+12) ?
The solution to 2/(x+3)-1/(x^2+7x+12) is (2x+7)/((x+3)(x+4))