Can you help me solve these questions?

Question

I can't seem to solve these fraction questions for x:

1) (x-1)/(x+5)=(x+7)/(x+8)

2) 3x-4         x-3
    ------     = -------
   2x-1          x+8

3) 4x-5           x+10
      ------     = -------
   1-6x              x-6

Answer 1

1). (x-1)/(x+5) = (x+7)/(x+8)

Cross multiplication.

(x - 1)(x + 8) = (x + 7)(x + 5)

Recall FOIL method: the product of two binomials is the sum of the products of the First terms, the Outer terms, the Inner terms and the Last terms.

x(x) + x(8) - 1(x) -1(8) = x(x) + x(5) + 7(x) +7(5)

x² + 8x - x - 8 = x² + 5x + 7x + 35

x² + 7x - 8 = x² + 12x + 35

Subtract x² from each side.

7x - 8 = 12x + 35

Subtract 7x from each side.

- 8 = 5x + 35

Add 8 to each side.

0 = 5x + 43

Subtract 43 from each side.

- 43 = 5x + 43 - 43

- 43 = 5x

Divide each side by 5.

- 8.6 = x

There fore x = - 8.6

Answer 2

2) (3x-4) / ( 2x-1) = (x-3) / (x+8)

Cross multiplication.

(3x - 4)(x + 8) = (x - 3)(2x - 1)

Recall FOIL method: the product of two binomials is the sum of the products of the First terms, the Outer terms, the Inner terms and the Last terms.

3x(x) + 3x(8) - 4(x) - 4(8) = x(2x) + x(-1) - 3(2x) - 3(-1)

3x² + 24x - 4x - 32 = 2x² - x - 6x + 3

3x² + 20x - 32 = 2x² - 7x + 3

Subtract 2x² from each side.

x² + 20x - 32 = -7x + 3

Add -7x to each side.

x² + 27x - 32 = 3

Subtract 3 from each side.

x² + 27x - 35 = 0

Comapre equation with standard from and write the coefficients.

a = 1, b = 27 and c = - 35

The quadratic formula: x = [-b + √(b² - 4ac)] / 2a

x = [ - 27 + √((27)² - 4(1)(-35))] / 2(1)

x = [ - 27 + √(729 + 140)] / 2

x = [ - 27 + √(869)] / 2

x = [ - 27 + √(869)] / 2 or x = [ - 27 - √(869)] / 2

There fore x = [ - 27 + √(869)] / 2 or x = [ - 27 - √(869)] / 2.

Answer 3

3). (4x - 5) / (1 - 6x) = (x +10) / (x - 6)

Cross multiplication.

(4x - 5)(x - 6) = (x + 10)(1 - 6x)

Recall FOIL method: the product of two binomials is the sum of the products of the First terms, the Outer terms, the Inner terms and the Last terms.

4x(x) + 4x(-6) - 5(x) -5(-6) = x(1) + x(-6x) + 10(1) +10(-6x)

4x² - 24x - 5x + 30 = x - 6x² + 10 - 60x

4x² - 29x + 30 = - 6x² + 10 - 59x

Add '6x²+59x'  to each side.

10x² + 30x + 30 = 10

Subtract 10 from each side.

10x² + 30x + 20 = 0

Divide each side by 10.

x² + 3x + 2 = 0

Now solve the factor method.

x² + 2x + x + 2 = 0

x(x + 2) + 1(x + 2) = 0

Take out common factors.

(x + 2)(x + 1) = 0

x + 2 = 0 or x + 1 = 0

x + 2 = 0

Subtract 2 from each side.

x = -2

x + 1 = 0

Subtract 1 from each side.

x = -1

There fore x = -2 or x = -1.