What is expand (x+4)/(2+x-6)+(x-3)/(2+7x+12) ?

The solution to expand (x+4)/(2+x-6)+(x-3)/(2+7x+12) is (8x^2+35x+68)/(7x^2-14x-56)

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expand (x+4)/(2+x-6)+(x-3)/(2+7x+12)

expand

\frac{x + 4}{2 + x - 6} + \frac{x - 3}{2 + 7 x + 12}

\frac{8 x ^{2} + 35 x + 68}{7 x ^{2} - 14 x - 56}

Solution steps

\frac{x + 4}{2 + x - 6} + \frac{x - 3}{2 + 7 x + 12}

2 + x - 6 = x - 4

= \frac{x + 4}{x - 4} + \frac{x - 3}{7 x + 2 + 12}

2 + 7 x + 12 = 7 x + 14

= \frac{x + 4}{x - 4} + \frac{x - 3}{7 x + 14}

Factor

7 x + 14 : 7 (x + 2)

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Since the denominators are equal, combine the fractions:

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

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

Expand

7 (x - 4) (x + 2) : 7 x^{2} - 14 x - 56

= \frac{7 ( x + 4 ) ( x + 2 ) + ( x - 3 ) ( x - 4 )}{7 x ^{2} - 14 x - 56}

Expand

(x + 4) \cdot 7 (x + 2) + (x - 3) (x - 4) : 8 x^{2} + 35 x + 68

= \frac{8 x ^{2} + 35 x + 68}{7 x ^{2} - 14 x - 56}

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

(3 x - 9 x^{2} - 6 x + 3) (\frac{1}{x})

(c = \frac{- y}{x} + x^{2}) x

(- 2.5099 + 6.2121 i)^{5}

(5 p + q) (5 p - q)

What is expand (x+4)/(2+x-6)+(x-3)/(2+7x+12) ?
The solution to expand (x+4)/(2+x-6)+(x-3)/(2+7x+12) is (8x^2+35x+68)/(7x^2-14x-56)