solve for x: 1/2x-3 + 1/x-5 = 1 - Maths - Quadratic Equations

Question

solve for x: 1/2x-3 + 1/x-5 = 1

Mayank Bhardwaj · Accepted Answer

Dear Student!

Here is the answer to your query.

$\frac{1}{2 x - 3} + \frac{1}{x - 5} = 1 \Rightarrow \frac{x - 5 + 2 x - 3}{(2 x - 3) (x - 5)} = 1 \Rightarrow 3 x - 8 = 2 x^{2} - 13 x + 15 \Rightarrow 2 x^{2} - 13 x - 3 x + 15 + 8 = 0 \Rightarrow 2 x^{2} - 16 x + 23 = 0$

On comparing the equation with general form ax² + bx + c = 0

We get

a = 2, b = –16, c = 23

On putting these values in the quadratic formula, we get

$x = \frac{16 \pm \sqrt{(- 16)^{2} - 4 \times 2 \times 23}}{2 \times 2} \Rightarrow x = \frac{16 \pm \sqrt{256 - 184}}{4} \Rightarrow x = 4 \pm \frac{\sqrt{72}}{4} = 4 \pm \frac{2 \sqrt{18}}{4} \Rightarrow x = 4 \pm \frac{\sqrt{18}}{2} and x = 4 - \frac{\sqrt{18}}{2}$

Cheers!

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