New Zealand
Level 7 - NCEA Level 2

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.

Question 1

Find the value of the expression $\frac{x+12}{x+2}$x+12x+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.

Worked Examples

Question 2

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

$\frac{4y-1}{y-1}$4y1y1

Question 3

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

$\frac{y}{y^3-43}$yy343

Question 4

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

$\frac{2x-9}{5}$2x95

Outcomes

M7-6

Manipulate rational, exponential, and logarithmic algebraic expressions

91261

Apply algebraic methods in solving problems