Methods to solve rational equation:
Rational equation:
A rational equation is an equation containing at least one rational expression.
Method 1:
The method for solving rational equations is to rewrite the rational expressions in terms of a common denominator. Then, since we know the numerators are equal, we can solve for the variable.
For example,
[tex]\frac{1}{2}=\frac{x}{2}\Rightarrow x=1[/tex]
This can be used for rational equations with polynomials too.
For example,
[tex]\frac{1+x}{x-3}=\frac{4}{x-3}\Rightarrow(1+x)=4 \Rightarrow x=3[/tex]
When the terms in a rational equation have unlike denominators, solving the equation will be as follows
[tex]\frac{x+2}{8}=\frac{3}{4}[/tex]
[tex]\Rightarrow\frac{x+2}{1}=\frac{3\times8}{4}\Rightarrow{x+2}=2\times3[/tex]
[tex]\Rightarrow{x+2}=6\Rightarrow x=6-2\Rightarrow x=4[/tex]
Method 2:
Another way of solving the above equation is by finding least common denominator (LCD)
[tex]\frac{x+2}{8}=\frac{3}{4}[/tex]
Factors of 4: [tex]1\times2\times2[/tex]
Factors of 8: [tex]1\times2\times2\times2[/tex]
The LCD of 4 and 8 is 8. So, we have to make the right hand side denominator as 8. This is done by the following step,
[tex]\Rightarrow\frac{x+2}{8}=\frac{3}{4}\times{2}{2}[/tex]
we get,
[tex]\Rightarrow\frac{x+2}{8}=\frac{6}{8}[/tex]
On cancelling 8 on both sides we get,
[tex]\Rightarrow(x+2)=6\rightarrow x=6-2\rightarrow x=4[/tex]
Hence, these are the ways to solve a rational equation.
