Question

How do you simplify `\frac { 2x + 3} { x ( x + 2) } = \frac { 7} { x + 2}`?

Answer 1

One should eliminate the denominators by multiplying both sides of the equation by `x(x+2)`. Then, one merely combines like terms, to obtain a solution (which is surely the simplest form).

Explanation:

Given: `\frac { 2x + 3} { x ( x + 2) } = \frac { 7} { x + 2}`

Multiply both sides of the equation by `x(x+2)`:

`2x+3 = 7x`

`5x = 3`

`x = 3/5 larr` This is the solution and the simplest form.

Check:

`(2(3/5)+3)/(3/5(3/5+2)) = 7/(3/5+2)`

`(2(3)+15)/(3(3/5+2)) = 7/(3/5+2)`

`(21)/(3(3/5+2)) = 7/(3/5+2)`

`7/(3/5+2) = 7/(3/5+2)`

This checks.