What is (j-7)/(j+6)-(2j+5)/(j^2+8j+12) ?

The solution to (j-7)/(j+6)-(2j+5)/(j^2+8j+12) is (j^2-7j-19)/((j+6)(j+2))

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simplify (j-7)/(j+6)-(2j+5)/(j^2+8j+12)

simplify

\frac{j - 7}{j + 6} - \frac{2 j + 5}{j ^{2} + 8 j + 12}

\frac{j ^{2} - 7 j - 19}{( j + 6 ) ( j + 2 )}

Solution steps

\frac{j - 7}{j + 6} - \frac{2 j + 5}{j ^{2} + 8 j + 12}

Least Common Multiplier of

j + 6, j^{2} + 8 j + 12 : (j + 6) (j + 2)

Adjust Fractions based on the LCM

= \frac{( j - 7 ) ( j + 2 )}{( j + 6 ) ( j + 2 )} - \frac{2 j + 5}{( j + 6 ) ( j + 2 )}

Apply the fraction rule:

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

= \frac{( j - 7 ) ( j + 2 ) - ( 2 j + 5 )}{( j + 6 ) ( j + 2 )}

Simplify

(j - 7) (j + 2) - (2 j + 5) : j^{2} - 7 j - 19

= \frac{j ^{2} - 7 j - 19}{( j + 6 ) ( j + 2 )}

(8 w^{4} + w^{3})^{2}

(x^{3} + 3)^{2}

(a + 1)^{3}

\frac{1}{9}

\frac{45}{5}

What is (j-7)/(j+6)-(2j+5)/(j^2+8j+12) ?
The solution to (j-7)/(j+6)-(2j+5)/(j^2+8j+12) is (j^2-7j-19)/((j+6)(j+2))