What is (14)/((x^2-4))-((6-x))/((x+2)) ?

The solution to (14)/((x^2-4))-((6-x))/((x+2)) is (x^2-8x+26)/((x+2)(x-2))

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simplify (14)/((x^2-4))-((6-x))/((x+2))

simplify

\frac{14}{( x ^{2} - 4 )} - \frac{( 6 - x )}{( x + 2 )}

\frac{x ^{2} - 8 x + 26}{( x + 2 ) ( x - 2 )}

Solution steps

\frac{14}{x ^{2} - 4} - \frac{6 - x}{x + 2}

Least Common Multiplier of

x^{2} - 4, x + 2 : (x + 2) (x - 2)

Adjust Fractions based on the LCM

= \frac{14}{( x + 2 ) ( x - 2 )} - \frac{( 6 - x ) ( x - 2 )}{( x + 2 ) ( x - 2 )}

Apply the fraction rule:

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

= \frac{14 - ( 6 - x ) ( x - 2 )}{( x + 2 ) ( x - 2 )}

Simplify

14 - (6 - x) (x - 2) : x^{2} - 8 x + 26

= \frac{x ^{2} - 8 x + 26}{( x + 2 ) ( x - 2 )}

(2 x)^{2} (x - x^{2}) - 4 x (- x^{3} + x^{2} - 5)

x^{2} + \frac{1}{7} x + \frac{1}{7}

(3 \cdot \frac{a}{2} + \frac{b}{4} - 2 c)^{2}

(\frac{2}{3} a - 3 \frac{b}{2} - 4 \frac{c}{5})^{2}

(x^{3} - 2 x^{2} + x - 1) (5 - x)

What is (14)/((x^2-4))-((6-x))/((x+2)) ?
The solution to (14)/((x^2-4))-((6-x))/((x+2)) is (x^2-8x+26)/((x+2)(x-2))