Question

Solve the following rational equation plz help!!

Answer 1

x =
`(9)/(4)`

Explanation:

Given

`(4x)/(x+1)` -
`(5)/(x)` =
`(4)/(x^2+x)` ← factor denominator

`(4x)/(x+1)` -
`(5)/(x)` =
`(4)/(x(x+1))`

[ x ≠ 0, x ≠ - 1 as these would make the terms undefined ]

Multiply through by x(x + 1)

4x² - 5(x + 1) = 4

4x² - 5x - 4 = 4 ( subtract 4 from both sides )

4x² - 5x - 9 = 0 ← in standard form

(x + 1)(4x - 9) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

4x - 9 = 0 ⇒ 4x = 9 ⇒ x =
`(9)/(4)`

However, x ≠ - 1 for reason given above, then

solution is x =
`(9)/(4)`