Equations with rational expressions

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

Question 3