Solving rational inequalities

Solving rational inequalities

Lessons

Steps to solving rational inequalities:

1. Rewrite in the form p(x)q(x)\frac{p(x)}{q(x)} > 00 (symbol can be different)

2. Solve p(x)=0p(x) = 0 and q(x)=0q(x) = 0

3. Put answers from step 2 on a number line and check end points and test values

  • 1.
    Introduction to solving rational inequalities

    i) What is a rational inequality?

    ii) How to solve rational inequality?

    iii) Section Overview


  • 2.
    Solving Rational Inequalities With One Fraction

    Solve

    a)
    x5x+1\frac{x-5}{x+1} > 00

    b)
    x2+5x+6x216\frac{x^{2}+5x+6}{x^{2}-16} < 00


  • 3.
    Solving Rational Inequalities With Two Fractions

    Solve

    a)
    x3x+26\frac{x-3}{x+2} \leq 6

    b)
    1x53xx5\frac{1}{x-5} \geq \frac{3x}{x-5}

    c)
    2x\frac{2}{x} < x5x12\frac{x}{5x - 12}


  • 4.
    Solving Rational Inequalities With Three Fractions

    Solve

    a)
    53x4x19\frac{5}{3x} - \frac{4}{x} \geq \frac{1}{-9}

    b)
    2yy212y+1+1y1\frac{2y}{y^{2}-1} \geq \frac{2}{y+1} + \frac{1}{y-1}