Question

Algebra question?

What is a positive value of `x` that satisfies `10/(x-2)-5/(x+1)=5/2`?

Answer 1

`x = 5`

Explanation:

Given: `10/(x-2) - 5/(x+1) = 5/2`

One way to solve is to find a common denominator :

`10/(x-2) * (2(x+1))/(2(x+1)) - 5/(x+1) * (2(x-2))/(2(x-2)) = 5/2 * ((x+1)(x-2))/((x+1)(x-2))`

Simplify:

`(20(x+1))/(2(x-2)(x+1))-(10(x-2))/(2(x-2)(x+1))=(5(x+1)(x-2)) /(2(x-2)(x+1))`

Since the denominators are all the same, we only need to work with the numerators to solve:

`20(x+1) - 10(x-2) = 5(x+1)(x-2)`

Distribute:

`20x + 20 - 10x + 20 = 5(x^2 + x - 2x -2)`

Add/Subtract like terms on both sides of the equation:

`10x + 40 = 5x^2 -5x -10`

Put the equation in `Ax^2 + Bx + C = 0` form:

`5x^2-15x-50 = 0`

Factor:

`5(x^2 - 3x - 10) = 0`

`5(x-5)(x+2) = 0`

`x = 5, -2`

A second way to solve is to multiply the equation by the common denominator:

`2(x-2)(x+1)[10/(x-2) - 5/(x+1) = 5/2]`

`2(x+1)*10 - 2(x-2)*5 = (x-2)(x+1)*5`

Distribute:

`20x + 20 - 10x + 20 = 5(x^2 +x -2x -2)`

Solve as above.