What is (2x+7)/(x-5)-5/(x^2-10x+25) ?

The solution to (2x+7)/(x-5)-5/(x^2-10x+25) is (2x^2-3x-40)/((x-5)^2)

Popular >

simplify (2x+7)/(x-5)-5/(x^2-10x+25)

simplify

\frac{2 x + 7}{x - 5} - \frac{5}{x ^{2} - 10 x + 25}

\frac{2 x ^{2} - 3 x - 40}{( x - 5 ) ^{2}}

Solution steps

\frac{2 x + 7}{x - 5} - \frac{5}{x ^{2} - 10 x + 25}

Least Common Multiplier of

x - 5, x^{2} - 10 x + 25 : (x - 5)^{2}

Adjust Fractions based on the LCM

= \frac{( 2 x + 7 ) ( x - 5 )}{( x - 5 ) ^{2}} - \frac{5}{( x - 5 ) ^{2}}

Apply the fraction rule:

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

= \frac{( 2 x + 7 ) ( x - 5 ) - 5}{( x - 5 ) ^{2}}

Simplify

(2 x + 7) (x - 5) - 5 : 2 x^{2} - 3 x - 40

= \frac{2 x ^{2} - 3 x - 40}{( x - 5 ) ^{2}}

- 81 - - 25 + 100 - - 1

\frac{5 + i}{4 - i}

4 x^{2} + 4

\frac{5 x + 25}{x ^{3} - x ^{2}} \cdot \frac{x ^{2} - 1}{x ^{2} + 6 x + 5}

(4 t^{5})^{3}

What is (2x+7)/(x-5)-5/(x^2-10x+25) ?
The solution to (2x+7)/(x-5)-5/(x^2-10x+25) is (2x^2-3x-40)/((x-5)^2)