 Equations with rational expressions

Lesson

We've already looked at how to solve equations, whether that be in one, two or three steps. As you know, equations can involve a number of different operations and there are different methods for solving equations so click here if you need a refresher.

In this chapter, we are going to look at examples of equations that involve addition and subtraction of algebraic terms, including ones with fractions.

Examples

Question 1

Solve $\frac{-7}{100}+\frac{x}{100}=\frac{7x}{100}+\frac{7}{100}$7100+x100=7x100+7100 for $x$x.

Think: How do we move these terms around to get $x$x by itself.

Do:

 $\frac{-7}{100}+\frac{x}{100}$−7100​+x100​ $=$= $\frac{7x}{100}+\frac{7}{100}$7x100​+7100​ Multiply all the terms by the common denominator, $100$100 $-7+x$−7+x $=$= $7x+7$7x+7 Rearrange the expression so all the $x$x terms are on one side $-7-7$−7−7 $=$= $7x-x$7x−x Now let's simplify $-14$−14 $=$= $6x$6x $\frac{-14}{6}$−146​ $=$= $x$x Make $x$x the subject and simplify the fraction $x$x $=$= $\frac{-7}{3}$−73​

Question 2

Solve the following equation: $5x-\frac{104}{5}=x$5x1045=x

Question 3

Solve the following equation: $\frac{5x}{3}-3=\frac{3x}{8}$5x33=3x8