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.

7 0

3 years ago

Factor completely 3a4y3 − 12a3y2 + 6a2y.

umka2103 [35]

<span>3a4y3 − 12a3y2 + 6a2y
=3a^2y (a^2y^2 - 4ay + 2)

answer is </span>3a^2y (a^2y^2 - 4ay + 2) (second choice)

3 0

3 years ago

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