5.05 Solving rational equations

Adaptive

Worksheet

Interactive practice questions

What values make a rational equation undefined?

Any value that makes a numerator in the equation equal to zero

Any value that is not a solution to the equation

Any value that makes a denominator in the equation equal to zero

Any value that makes both the numerator and denominator equal to zero

Medium

< 1min

For what values of $a$a is the following rational equation undefined?

$\frac{4}{a+9}-\frac{3a}{\left(a+2\right)\left(a+1\right)}=0$4a+9−3a(a+2)(a+1)=0

Medium

4min

For what values of $y$y is the following rational equation undefined?

$\frac{8}{y}+\frac{9}{y-7}=\frac{22}{y^2+y}$8y+9y−7=22y2+y

Medium

3min

For what values of $p$p is the following rational equation undefined?

$-\frac{8}{p-7}-\frac{9}{p}=-\frac{3}{p^2-2p}$−8p−7−9p=−3p2−2p

Medium

3min

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.