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4 votes
(x)/(x-2)+(x-1)/(x+1)=-1

2 Answers

7 votes

Answer:

x = 0 or x = 1

Explanation:

(x)/(x - 2) + (x - 1)/(x + 1) = -1

The LCD is (x - 2)(x + 1).

Multiply both sides of the equation by the LCD.

(x - 2)(x + 1) × (x)/(x - 2) + (x - 2)(x + 1) × (x - 1)/(x + 1) = (x - 2)(x + 1) × (-1)

The factors in bold cancel out of each product.

x(x + 1) + (x - 2)(x - 1) = -(x - 2)(x + 1)

x² + x + x² - x - 2x + 2 = -(x² + x - 2x - 2)

2x² - 2x + 2 = -x² + x + 2

3x² - 3x = 0

3x(x - 1) = 0

x = 0 or x = 1

The restrictions on the domain are:

x - 2 = 0

x = 2

x + 1 = 0

x = -1

Since our solutions do not include the excluded values, x = 2 and x = -1, both solutions x = 0 and x = 1 are valid.

Answer: x = 0 or x = 1

User Danation
by
7.6k points
4 votes

Answer:


x=0 and
x=1

Explanation:


(x)/(x-2)+(x-1)/(x+1)=-1


(x(x+1))/((x-2)(x+1))+((x-2)(x-1))/((x-2)(x+1))=-1


(x(x+1)+(x-2)(x-1))/((x-2)(x+1))=-1


x(x+1)+(x-2)(x-1)=-(x-2)(x+1)


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


2x^2-2x+2=-x^2+x+2


3x^2-2x+2=x+2


3x^2-3x=0


3x(x-1)=0


x=0 and
x=1

User Ragnar Lothbrok
by
7.9k points

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