Question

Solve the given nonlinear inequality. Write the solution set using interval notation.

x2 − 3x + 4
x + 1
≤ 1

Answer 1

x-2/3x+4-6x/x+1?
I am assuming the question is (x - 2)/(3x + 4) - 6x/(x + 1)
(x - 2)/(3x + 4) - 6x/(x + 1) = 0
Mulitply both terms by (3x + 4)
(X - 2)(3x + 4) /(3x + 4) - 6x(3x + 4)/(x + 1) = 0
Simplify
(x - 2) - 6x(3x + 4)/(x + 1) = 0
Mulitply both terms by (x + 1)
(x - 2)(X + 1) - 6x(x + 1)(3x + 4)/(x + 1)
Simplify
x - 2)(X + 1) - 6x(3x + 4) = 0
Muliply out
x^2 - x - 2 - 18x^2 -24x = 0
Collect like terms
-17x^2 -25x -2 = 0
Multiply by -1
17x^2 + 25x + 2 = 0