What is 4/(x^2-3x+4)+3/(x^2-16)-7/(x^2+5x+4) ?

The solution to 4/(x^2-3x+4)+3/(x^2-16)-7/(x^2+5x+4) is (47x^2-173x+60)/((x+4)(x-4)(x+1)(x^2-3x+4))

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simplify 4/(x^2-3x+4)+3/(x^2-16)-7/(x^2+5x+4)

simplify

\frac{4}{x ^{2} - 3 x + 4} + \frac{3}{x ^{2} - 16} - \frac{7}{x ^{2} + 5 x + 4}

\frac{47 x ^{2} - 173 x + 60}{( x + 4 ) ( x - 4 ) ( x + 1 ) ( x ^{2} - 3 x + 4 )}

Solution steps

\frac{4}{x ^{2} - 3 x + 4} + \frac{3}{x ^{2} - 16} - \frac{7}{x ^{2} + 5 x + 4}

Least Common Multiplier of

x^{2} - 3 x + 4, x^{2} - 16, x^{2} + 5 x + 4 : (x + 4) (x - 4) (x + 1) (x^{2} - 3 x + 4)

Adjust Fractions based on the LCM

= \frac{4 ( x + 4 ) ( x - 4 ) ( x + 1 )}{( x + 4 ) ( x - 4 ) ( x + 1 ) ( x ^{2} - 3 x + 4 )} + \frac{3 ( x + 1 ) ( x ^{2} - 3 x + 4 )}{( x + 4 ) ( x - 4 ) ( x + 1 ) ( x ^{2} - 3 x + 4 )} - \frac{7 ( x - 4 ) ( x ^{2} - 3 x + 4 )}{( x + 4 ) ( x - 4 ) ( x + 1 ) ( x ^{2} - 3 x + 4 )}

Apply the fraction rule:

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

= \frac{4 ( x + 4 ) ( x - 4 ) ( x + 1 ) + 3 ( x + 1 ) ( x ^{2} - 3 x + 4 ) - 7 ( x - 4 ) ( x ^{2} - 3 x + 4 )}{( x + 4 ) ( x - 4 ) ( x + 1 ) ( x ^{2} - 3 x + 4 )}

Simplify

4 (x + 4) (x - 4) (x + 1) + 3 (x + 1) (x^{2} - 3 x + 4) - 7 (x - 4) (x^{2} - 3 x + 4) : 47 x^{2} - 173 x + 60

= \frac{47 x ^{2} - 173 x + 60}{( x + 4 ) ( x - 4 ) ( x + 1 ) ( x ^{2} - 3 x + 4 )}

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

\frac{100 \cdot 15 \cdot 12 \cdot 2 \cdot 7}{9 \cdot 40 \cdot 25 \cdot 14}

\frac{( - 3 + i ) ^{6}}{( 1 - i ) ^{10}}

\frac{( 6 ^{3} \cdot 6 ^{2} ) ^{2}}{( 6 ^{4} ) ^{- 2}}

What is 4/(x^2-3x+4)+3/(x^2-16)-7/(x^2+5x+4) ?
The solution to 4/(x^2-3x+4)+3/(x^2-16)-7/(x^2+5x+4) is (47x^2-173x+60)/((x+4)(x-4)(x+1)(x^2-3x+4))