Question

x-2/x2+2x-35 + 1/x-5 = x-3/x2+2x-35

Answer 1

The solution to the given equation is x = -8

Solving Equations

From the question, we are to solve the given equation

The given equation is

$\frac{x-2}{x^{2} +2x-35}+\frac{1}{x-5}=\frac{x-3}{x^{2} +2x-35}$

First, simplify x² +2x -35 as a product of two binomials

x² +2x -35

x² +7x -5x -35

x(x +7) -5(x +7)

(x -5)(x +7)

Thus,

The equation becomes

$\frac{x-2}{(x-5)(x+7)}+\frac{1}{x-5}=\frac{x-3}{(x-5)(x+7)}$

Multiply through by (x -5)(x +7)

$(x-5)(x+7) \times \frac {x-2}{(x-5)(x+7))}+ (x-5)(x+7) \times \frac{1}{x-5} = (x-5)(x+7) \times \frac{x-3}{(x-5)(x+7)}$

$(x-2) +1(x +7)=x-3$

(x -2) + (x +7) = x -3

x - 2 + x + 7 = x - 3

Collect like terms

x + x - x = -3 + 2 - 7

x = -8

Hence, the solution to the given equation is x = -8

Learn more on Solving equations here: https://brainly.com/question/13622223

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