What is 1/(x^2-14x+49)-(2x)/(x-7) ?

The solution to 1/(x^2-14x+49)-(2x)/(x-7) is (1-2x^2+14x)/((x-7)^2)

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simplify 1/(x^2-14x+49)-(2x)/(x-7)

simplify

\frac{1}{x ^{2} - 14 x + 49} - \frac{2 x}{x - 7}

\frac{1 - 2 x ^{2} + 14 x}{( x - 7 ) ^{2}}

Solution steps

\frac{1}{x ^{2} - 14 x + 49} - \frac{2 x}{x - 7}

Least Common Multiplier of

x^{2} - 14 x + 49, x - 7 : (x - 7)^{2}

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

1 - 2 x (x - 7) : 1 - 2 x^{2} + 14 x

= \frac{1 - 2 x ^{2} + 14 x}{( x - 7 ) ^{2}}

\frac{6}{60}

(x - y)^{2}

(h^{2} + 1 + 1) (h^{2} + 1 - 1)

\frac{2}{3} \times 6

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

What is 1/(x^2-14x+49)-(2x)/(x-7) ?
The solution to 1/(x^2-14x+49)-(2x)/(x-7) is (1-2x^2+14x)/((x-7)^2)