Question

5) (x - 1)/(x + 2) = (2x - 1)/(2x + 1) 6) (3x - 5)/(x - 1) - (2x - 5)/(x - 2) = 1 7) (x ^ 2 + 9)/(x ^ 2 - 1) = (x - 2)/(x + 1) - 5/(1 - x) 8) 1/(x ^ 2 - 6x) + 1/(x ^ 2 + 6x) = (2x)/(x ^ 2 - 36)

Answer 1

Ответ:

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

Cross-multiply: (x - 1)(2x + 1) = (2x - 1)(x + 2)

Expand both sides: 2x^2 - x - 1 = 2x^2 + 3x - 2

Simplify: -4x = -1

Solve for x: x = 1/4

2) (3x - 5)/(x - 1) - (2x - 5)/(x - 2) = 1

Find a common denominator: (3x - 5)(x - 2) - (2x - 5)(x - 1) = (x - 1)(x - 2)

Expand both sides: 3x^2 - 13x + 10 - 2x^2 + 7x - 5 = x^2 - 3x + 2

Simplify: x^2 - 6x + 8 = x^2 - 3x +2

Solve for x: -3x = -6

Solve for x: x = 2

3) (x ^ 2 + 9)/(x ^ 2 - 1) = (x - 2)/(x + 1) - 5/(1 - x)

Find a common denominator: (x ^ 2 + 9)(x + 1) - (x - 2)(1 - x) = (x ^ 2 - 1)(1 - x)

Expand both sides: x^3 + 10x + 9 - x^2 + 3x - 2 = x^3 - x^2 - x + 1

Simplify: 2x^2 + 13x + 7 = x^3 - x^2 - x + 1

4) 1/(x ^ 2 - 6x) + 1/(x ^ 2 + 6x) = (2x)/(x ^ 2 - 36)

Find a common denominator: (x + 6) + (x - 6) = 2x(x + 6)(x - 6)

Expand both sides: 2x = 2x^3 - 72x

Simplify: 2x^3 - 74x = 0