Question

solve for x(in terms of a and b) a/x-b + b/x-a. =2. x is not equal to a,b. and the answer should be a+b,a+b/2. please solve to whole equation i want the solution .

Answer 1

Refer to attachment for soln

Hope it helps

Answer 2

Value is $\bf \red{x = \frac{a + b}{2}}$ and $\bf \red{x = a + b}$.

Given:

• $\frac{a}{x - b} + \frac{b}{x - a} = 2 \: ;x \neq \: a ,\: b$

To find:

• Value of x.

Solution:

Identity to be used:

$\bf {x}^{2} +2xy + {y}^{2} = (x+y)^2$

Step 1:

Take LCM in LHS.

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

cross multiply.

$a(x - a) + b(x - b) = 2(x - a)(x - b)$

Open bracket.

$ax - {a}^{2} + bx - {b}^{2} = 2( {x}^{2} - (a + b)x + ab)$

or

$2 {x}^{2} - 2ax - 2bx + 2ab - ax - bx + {a}^{2} + {b}^{2} = 0$

or

$2 {x}^{2} - 3ax - 3bx + {a}^{2} +2ab + {b}^{2} = 0$

or

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

Step 2:

Solve the quadratic equation.

Split the middle term.

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

or

$2x[x - (a + b)] - (a + b)[x - (a + b)] = 0$

or

$[2x - (a + b)][x - (a + b)] = 0$

or

$2x - (a + b) = 0$

or

$2x = a + b$

or

$\bf \red{x = \frac{a + b}{2}}$

and

$x - (a + b) = 0$

or

$\bf \red{x = a + b}$

Thus,

Value of x is (a+b)/2 and (a+b).

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