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nevsk [136]
3 years ago
12

Explain how you know which method you should use to solve a rational equation.

Mathematics
1 answer:
notsponge [240]3 years ago
7 0

<u>Methods to solve rational equation:</u>

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,

\frac{1}{2}=\frac{x}{2}\Rightarrow x=1

This can be used for rational equations with polynomials too.

For example,

\frac{1+x}{x-3}=\frac{4}{x-3}\Rightarrow(1+x)=4 \Rightarrow x=3

When the terms in a rational equation have unlike denominators, solving the equation will be as follows

\frac{x+2}{8}=\frac{3}{4}

\Rightarrow\frac{x+2}{1}=\frac{3\times8}{4}\Rightarrow{x+2}=2\times3

\Rightarrow{x+2}=6\Rightarrow x=6-2\Rightarrow x=4

Method 2:

Another way of solving the above equation is by finding least common denominator (LCD)

\frac{x+2}{8}=\frac{3}{4}

Factors of 4: 1\times2\times2

Factors of 8: 1\times2\times2\times2

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,

\Rightarrow\frac{x+2}{8}=\frac{3}{4}\times{2}{2}

we get,

\Rightarrow\frac{x+2}{8}=\frac{6}{8}

On cancelling 8 on both sides we get,

\Rightarrow(x+2)=6\rightarrow x=6-2\rightarrow x=4

Hence, these are the ways to solve a rational equation.

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