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^3-j^2-37j-54)/((j-6)(j+2)(j+6))

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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 ^{3} - j ^{2} - 37 j - 54}{( j - 6 ) ( j + 2 ) ( j + 6 )}

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) (j + 6)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

(j - 7) (j + 2) (j + 6) - (2 j + 5) (j - 6) : j^{3} - j^{2} - 37 j - 54

= \frac{j ^{3} - j ^{2} - 37 j - 54}{( j - 6 ) ( j + 2 ) ( j + 6 )}

16 \times 16 \times 16

x^{4} y^{2} + 2 x^{2} + y^{4}

\frac{2}{5} \times \frac{3}{8}

3 \times \frac{2}{7}

56 - 27 x - 18 x^{2}

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^3-j^2-37j-54)/((j-6)(j+2)(j+6))