Question

solve 4x/(x-2) -(3x)/(x-1)=15/2​

Answer 1

Answer:

let x-1 be a and x-2 be B.

4a-3xb=15/2

2a=(15+3xb)/4

a=(15+3xb)/4

Hope it helps u

Answer 2

Given,

4x/(x-2) -(3x)/(x-1)=15/2​

To Find,

The value of x =?

Solution,

We can solve the question using the following steps:

The given equation is,

$\frac{4x}{x - 2} - \frac{3x}{x - 1} = \frac{15}{2}$

Taking the LHS,

$\frac{4x}{x - 2} - \frac{3x}{x - 1}$

⇒$\frac{(4x^{2} - 4x) - (3x^{2} - 6x)}{(x-2)(x-1)}$

⇒$\frac{x^{2} + 2x }{x^{2} -x-2x +2}$

⇒$\frac{x^{2} + 2x }{x^{2} -3x+2}$

Now,

$\frac{x^{2} + 2x }{x^{2} -3x+2} = \frac{15}{2}$

⇒$2x^{2} + 4x = 15x^{2} - 45x + 30$

⇒$13x^{2} - 49x + 30 = 0$

Solving the above quadratic equation,

$13x^{2} - 49x + 30 = 0$

$13x^{2} - 39x - 10x + 30 = 0$

$13x(x - 3) - 10(x - 3) = 0$

$(13x - 10)(x - 3) = 0$

$13x - 10 = 0, x - 3 =0$

$x = \frac{10}{13} , x = 3$

Hence, the value of x is equal to 10/13, 3.