Question

Solve the rational equation algebraically. Write the steps.

Answer 1

1) x = -5 or 9; 2) x =7 or 0

Explanation:

1)
`(a)/(b) = (c)/(d); ad = bc`

So just multiply to get

`8x + 48 = x^2 + 4x + 3\\0 = x^2 - 4x - 45\\(x + 5)(x - 9) = 0`

2) Multiply by the LCM, in this case it is 2x - 6 as (x-3)(2) = 2x -6.

You get:

`(2)(x)+(x)\left(x-3\right)=6x\\2x + x^2 -3x -6x = 0\\x^2 - 7x = 0\\take\ out\ the\ x\\x(x-7) = 0\\x = 0 \ or \ x = 7`