What is (x-1)/(x-2)-(x^2+4x-4)/(x^2+4x-12) ?

The solution to (x-1)/(x-2)-(x^2+4x-4)/(x^2+4x-12) is 1/(x+6)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (x-1)/(x-2)-(x^2+4x-4)/(x^2+4x-12)

simplify

\frac{x - 1}{x - 2} - \frac{x ^{2} + 4 x - 4}{x ^{2} + 4 x - 12}

\frac{1}{x + 6}

Solution steps

\frac{x - 1}{x - 2} - \frac{x ^{2} + 4 x - 4}{x ^{2} + 4 x - 12}

Least Common Multiplier of

x - 2, x^{2} + 4 x - 12 : (x - 2) (x + 6)

Adjust Fractions based on the LCM

= \frac{( x - 1 ) ( x + 6 )}{( x - 2 ) ( x + 6 )} - \frac{x ^{2} + 4 x - 4}{( x - 2 ) ( x + 6 )}

Apply the fraction rule:

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

= \frac{( x - 1 ) ( x + 6 ) - ( x ^{2} + 4 x - 4 )}{( x - 2 ) ( x + 6 )}

Simplify

(x - 1) (x + 6) - (x^{2} + 4 x - 4) : x - 2

= \frac{x - 2}{( x - 2 ) ( x + 6 )}

Cancel the common factor:

x - 2

= \frac{1}{x + 6}

lo g_{\frac{5}{2}} (\frac{2}{5})

\frac{1}{2} + \frac{1}{\frac{1}{2}}

2 (9.8)

(x^{2} + 3 x - 1) (x^{2} - 3 x - 7)

x^{6} - 6 x^{5} + 24 x^{3} - x^{2} + 30 x

What is (x-1)/(x-2)-(x^2+4x-4)/(x^2+4x-12) ?
The solution to (x-1)/(x-2)-(x^2+4x-4)/(x^2+4x-12) is 1/(x+6)