What is (x+8)/(x^2-4x+4)+(3x-2)/(x^2-4) ?

The solution to (x+8)/(x^2-4x+4)+(3x-2)/(x^2-4) is (4x^2+2x+20)/((x-2)^2(x+2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (x+8)/(x^2-4x+4)+(3x-2)/(x^2-4)

simplify

\frac{x + 8}{x ^{2} - 4 x + 4} + \frac{3 x - 2}{x ^{2} - 4}

\frac{4 x ^{2} + 2 x + 20}{( x - 2 ) ^{2} ( x + 2 )}

Solution steps

\frac{x + 8}{x ^{2} - 4 x + 4} + \frac{3 x - 2}{x ^{2} - 4}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{( x + 8 ) ( x + 2 )}{( x - 2 ) ^{2} ( x + 2 )} + \frac{( 3 x - 2 ) ( x - 2 )}{( x - 2 ) ^{2} ( x + 2 )}

Apply the fraction rule:

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

= \frac{( x + 8 ) ( x + 2 ) + ( 3 x - 2 ) ( x - 2 )}{( x - 2 ) ^{2} ( x + 2 )}

Simplify

(x + 8) (x + 2) + (3 x - 2) (x - 2) : 4 x^{2} + 2 x + 20

= \frac{4 x ^{2} + 2 x + 20}{( x - 2 ) ^{2} ( x + 2 )}

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

\frac{5 x ^{2} - 10 x}{5 x}

x^{4} + 6 x^{2} + 8

4 (\frac{y}{2} - 2) - (8 + y)

26 (43 - 36)

What is (x+8)/(x^2-4x+4)+(3x-2)/(x^2-4) ?
The solution to (x+8)/(x^2-4x+4)+(3x-2)/(x^2-4) is (4x^2+2x+20)/((x-2)^2(x+2))