Algebra

NZ Level 7 (NZC) Level 2 (NCEA)

Evaluate rational expressions

Lesson

We've looked at how to substitute values into algebraic expressions. We just replace any pronumeral in the expression with the given numerical value. In this chapter, we are going to revisit this same process and extend it by substituting values into algebraic fractions as well.

Consider the following problem.

Find the value of the expression $\frac{x+12}{x+2}$`x`+12`x`+2 when $x=3$`x`=3.

**Think:** we want to replace $x$`x` with the value of $3$3 and then simplify the expression following the usual order of operations.

Do: |
$\frac{x+12}{x+2}$x+12x+2 |
$=$= | $\frac{\left(3\right)+12}{\left(3\right)+2}$(3)+12(3)+2 |

$=$= | $\frac{15}{5}$155 | ||

$=$= | $3$3 |

Some worked examples are provided below.

Find the value of the expression when $y=6$`y`=6:

$\frac{4y-1}{y-1}$4`y`−1`y`−1

Find the value of the expression when $y=4$`y`=4:

$\frac{y}{y^3-43}$`y``y`3−43

Find the value of the expression when $x=\frac{29}{2}$`x`=292:

$\frac{2x-9}{5}$2`x`−95

Manipulate rational, exponential, and logarithmic algebraic expressions

Apply algebraic methods in solving problems