What is (q^2+8q+14)/(q^2+6q+8)-1/(q+2)-1 ?

The solution to (q^2+8q+14)/(q^2+6q+8)-1/(q+2)-1 is 1/(q+4)

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simplify (q^2+8q+14)/(q^2+6q+8)-1/(q+2)-1

simplify

\frac{q ^{2} + 8 q + 14}{q ^{2} + 6 q + 8} - \frac{1}{q + 2} - 1

\frac{1}{q + 4}

Solution steps

\frac{q ^{2} + 8 q + 14}{q ^{2} + 6 q + 8} - \frac{1}{q + 2} - 1

Join

\frac{q ^{2} + 8 q + 14}{q ^{2} + 6 q + 8} - \frac{1}{q + 2} : \frac{q ^{2} + 8 q + 14 - ( q + 4 )}{( q + 2 ) ( q + 4 )}

= \frac{q ^{2} + 8 q + 14 - ( q + 4 )}{( q + 2 ) ( q + 4 )} - 1

Apply the fraction rule:

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

= \frac{- 1 \cdot ( q + 2 ) ( q + 4 ) + q ^{2} + 8 q + 14 - ( q + 4 )}{( q + 2 ) ( q + 4 )}

Apply rule:

1 \cdot a = a

- 1 \cdot (q + 2) (q + 4) = - (q + 2) (q + 4)

= \frac{- ( q + 2 ) ( q + 4 ) + q ^{2} + 8 q + 14 - ( q + 4 )}{( q + 2 ) ( q + 4 )}

Simplify

- (q + 2) (q + 4) + q^{2} + 8 q + 14 - (q + 4) : q + 2

= \frac{q + 2}{( q + 2 ) ( q + 4 )}

Cancel the common factor:

q + 2

= \frac{1}{q + 4}

\frac{2}{3} + \frac{1}{4} \times \frac{2}{5} - \frac{3}{4} + \frac{5}{2}

\frac{x ^{2} + y ^{2}}{x ^{2} + y ^{2}}

\frac{7}{12} \div \frac{2}{9}

\frac{x ^{3} - 2 x ^{2} + x - 2}{x ^{2} - 4}

(- y + 4) (2 y - 1)

What is (q^2+8q+14)/(q^2+6q+8)-1/(q+2)-1 ?
The solution to (q^2+8q+14)/(q^2+6q+8)-1/(q+2)-1 is 1/(q+4)