How do you add $\frac{x - 4}{2 x^{2} + 9 x - 5} + \frac{x + 3}{x^{2} + 5 x}$ $\frac { x - 4} { 2x ^ { 2} + 9x - 5} + \frac { x + 3} { x ^ { 2} + 5x }$ ?

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How do you add $\frac{x - 4}{2 x^{2} + 9 x - 5} + \frac{x + 3}{x^{2} + 5 x}$ $\frac { x - 4} { 2x ^ { 2} + 9x - 5} + \frac { x + 3} { x ^ { 2} + 5x }$ ?

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Answer 1 · 2016-12-07T04:56:26

$\frac{3 x^{2} + x - 3}{(x) (x + 5) (2 x - 1)}$ $(3x^2 + x - 3)/((x)(x + 5)(2x- 1))$

Explanation:

Factor the denominators to discover the least common denominator (LCD).

$2 x^{2} + 9 x - 5 = 2 x^{2} + 10 x - x - 5 = 2 x (x + 5) - (x + 5) = (2 x - 1) (x + 5)$ $2x^2 + 9x - 5 = 2x^2 + 10x - x - 5 = 2x(x + 5) - (x + 5) = (2x- 1)(x + 5)$

$x^{2} + 5 x = x (x + 5)$ $x^2 + 5x= x(x + 5)$

Therefore, the LCD is $(x) (x + 5) (2 x - 1)$ $color(green)((x)(x + 5)(2x - 1))$ .

$\Rightarrow \frac{x (x - 4)}{(x) (x + 5) (2 x - 1)} + \frac{(x + 3) (2 x - 1)}{(x) (x + 5) (2 x - 1)}$ $=>(x(x- 4))/((x)(x+ 5)(2x- 1)) + ((x+ 3)(2x- 1))/((x)(x + 5)(2x- 1))$

$\Rightarrow \frac{x^{2} - 4 x + 2 x^{2} + 6 x - x - 3}{(x) (x + 5) (2 x - 1)}$ $=>(x^2 -4x + 2x^2 + 6x- x - 3)/((x)(x+ 5)(2x - 1))$

$\Rightarrow \frac{3 x^{2} + x - 3}{(x) (x + 5) (2 x - 1)}$ $=>(3x^2 + x - 3)/((x)(x + 5)(2x- 1))$

Hopefully this helps!

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How do you add $\frac{x - 4}{2 x^{2} + 9 x - 5} + \frac{x + 3}{x^{2} + 5 x}$ $\frac { x - 4} { 2x ^ { 2} + 9x - 5} + \frac { x + 3} { x ^ { 2} + 5x }$ ?

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How do you add $\frac{x - 4}{2 x^{2} + 9 x - 5} + \frac{x + 3}{x^{2} + 5 x}$ $\frac { x - 4} { 2x ^ { 2} + 9x - 5} + \frac { x + 3} { x ^ { 2} + 5x }$ ?