Question

How do you solve `(x-6/5)/x-(x-10 1/2)/(x-5)=(x+21)/(x^2-5x)`?

Answer 1

`x = 50/11`

Explanation:

Rewriting the right side of the equation,
The common denominator is `x^2 - 5x`

`((x-5)(x-6/5))/(x^2 - 5x) - (x(x-10.5))/(x^2 - 5x) = (x+21)/(x^2 - 5x)`

Multiplying both sides of the equation by `x^2 - 5x`,

`(x-5)(x-6/5) - x(x-10.5) = x+21`

Simplifying further,
`(x^2 - 31/5x + 6) - (x^2 - 10.5x) = x+21`
`x^2 - 31/5x - x^2 + 10.5x - x=21-6`
`-33/10x = 15`
`x = 50/11`