Solving rational equations

Solving rational equations

In this lesson, we will learn how to state the non-permissible value(s) of rational equations and how to solve them algebraically.

Lessons

Always find the non-permissible values before solving the rational equations as some answers might have to be rejected.
  • 1.
    Solve the following rational equations:
    a)
    33x=1+1x3-\frac{3}{x}=1+\frac{1}{x}

    b)
    2x+15x=132x+\frac{15}{x}=13


  • 2.
    Solving Rational Equations by cross multiplying
    State the non-permissible values for the variable x, then solve algebraically.
    a)
    8x+4=3x1 \frac{8}{x+4}=\frac{3}{x-1}

    b)
    2x26x1=3x+49x+5 \frac{2x-2}{6x-1}=\frac{3x+4}{9x+5}


  • 3.
    Solve
    2x9+20x+9=80x281 \frac{2}{x-9}+\frac{20}{x+9}=\frac{80}{x^2-81}

  • 4.
    Solve the following equations algebraically:
    a)
    2x+2+3x2=1\frac{2}{x+2}+\frac{3}{x-2}=1

    b)
    2t3t13t+1t+2=1\frac{2t-3}{t-1}-\frac{3t+1}{t+2}=-1


  • 5.
    Solving Rational Equations by factoring
    State the non-permissible values for the variables, then solve algebraically.
    a)
    x25x+4(x1)=4 \frac{x^2-5x+4}{(x-1)}=-4

    b)
    x1x21=12x3\frac{x-1}{x^2-1}=\frac{1}{2x-3}