Evaluate rational expressions
We've looked at how to substitute values into algebraic expressions. We just replace any variable 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}$4y−1y−1
Question 3
Find the value of the expression when $y=4$y=4:
$\frac{y}{y^3-43}$yy3−43
Question 4
Find the value of the expression when $x=\frac{29}{2}$x=292:
$\frac{2x-9}{5}$2x−95