What is expand (x+2)/((x+3)(x-4))+(x-1)/(2+2x) ?

The solution to expand (x+2)/((x+3)(x-4))+(x-1)/(2+2x) is (x^3-5x+16)/(2x^3-26x-24)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (x+2)/((x+3)(x-4))+(x-1)/(2+2x)

expand

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

\frac{x ^{3} - 5 x + 16}{2 x ^{3} - 26 x - 24}

Solution steps

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

Expand

(x + 3) (x - 4) : x^{2} - x - 12

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

Factor

x^{2} - x - 12 : (x + 3) (x - 4)

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

Factor

2 x + 2 : 2 (x + 1)

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

Least Common Multiplier of

(x + 3) (x - 4), 2 (x + 1) : 2 (x + 3) (x - 4) (x + 1)

Adjust Fractions based on the LCM

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

Since the denominators are equal, combine the fractions:

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

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

Expand

2 (x + 3) (x - 4) (x + 1) : 2 x^{3} - 26 x - 24

= \frac{2 ( x + 2 ) ( x + 1 ) + ( x - 1 ) ( x + 3 ) ( x - 4 )}{2 x ^{3} - 26 x - 24}

Expand

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

= \frac{x ^{3} - 5 x + 16}{2 x ^{3} - 26 x - 24}

6 x^{3} δ (x - 2)

(4 - x) ln (x + 7)

(1 + x^{2}) \frac{d y}{d x} + x y

(x - \frac{1}{x})^{12}

\frac{d}{d v} ((p) (p + \frac{4.1}{v ^{2}}) (v - 8.5))

What is expand (x+2)/((x+3)(x-4))+(x-1)/(2+2x) ?
The solution to expand (x+2)/((x+3)(x-4))+(x-1)/(2+2x) is (x^3-5x+16)/(2x^3-26x-24)