Solve (x-b)/(x-a) - (x-a)/(x-b) = (2(a-b))/(x-(a b))

Question

Simplify the expression

\approx - b^{2} a - b a^{2} + 2 x ba + 2 ba - x b - x a = 0, x \approx b - a = 0, x

Evaluate

\frac{x - b}{x - a} - \frac{x - a}{x - b} = \frac{2 ( a - b )}{x - ab}, x

Calculate

More Steps

Evaluate

\frac{x - b}{x - a} - \frac{x - a}{x - b} = \frac{2 ( a - b )}{x - ab}

Multiply both sides of the equation by LCD

(\frac{x - b}{x - a} - \frac{x - a}{x - b}) (x - a) (x - b) (x - ab) = \frac{2 ( a - b )}{x - ab} \times (x - a) (x - b) (x - ab)

Simplify the equation

More Steps

- 2 x^{2} b + 2 x b^{2} a + b^{2} x - b^{3} a + 2 x^{2} a - 2 x a^{2} b - a^{2} x + a^{3} b = \frac{2 ( a - b )}{x - ab} \times (x - a) (x - b) (x - ab)

Simplify the equation

More Steps

- 2 x^{2} b + 2 x b^{2} a + b^{2} x - b^{3} a + 2 x^{2} a - 2 x a^{2} b - a^{2} x + a^{3} b = 2 a x^{2} - 2 a^{2} x + 2 a^{2} b - 2 b x^{2} + 2 b^{2} x - 2 b^{2} a

Cancel equal terms on both sides of the expression

2 x b^{2} a + b^{2} x - b^{3} a - 2 x a^{2} b - a^{2} x + a^{3} b = - 2 a^{2} x + 2 a^{2} b + 2 b^{2} x - 2 b^{2} a

Move the expression to the left side

2 x b^{2} a + b^{2} x - b^{3} a - 2 x a^{2} b - a^{2} x + a^{3} b - (- 2 a^{2} x + 2 a^{2} b + 2 b^{2} x - 2 b^{2} a) = 0

Calculate the sum or difference

More Steps

2 x b^{2} a - b^{2} x - b^{3} a - 2 x a^{2} b + a^{2} x + a^{3} b - 2 a^{2} b + 2 b^{2} a = 0

Factor the expression

(- b^{2} a - b a^{2} + 2 x ba + 2 ba - x b - x a) (b - a) = 0

Separate the equation into 2 possible cases

- b^{2} a - b a^{2} + 2 x ba + 2 ba - x b - x a = 0 b - a = 0

- b^{2} a - b a^{2} + 2 x ba + 2 ba - x b - x a = 0 b - a = 0, x

Solution

\approx - b^{2} a - b a^{2} + 2 x ba + 2 ba - x b - x a = 0, x \approx b - a = 0, x

Show Solution

a = x, a = \frac{x}{b}, b = x

Show Solution