How to Simplify Rational Expressions

Step-by-Step Guide

1. 1

   Step 1: Evaluate the expression.

   To use this method, you should see a monomial in the numerator and in the denominator of your rational expression.
   
   A monomial is a polynomial with one term.For example, the expression 4x16x2{\displaystyle {\frac {4x}{16x^{2}}}} has one term in the numerator, and one term in the denominator.
   
   Thus, each is a monomial.
   
   The expression 4x+416x2−2{\displaystyle {\frac {4x+4}{16x^{2}-2}}} has two binomials and thus cannot be solved using this method.
2. 2

   Step 2: Factor the numerator.

   To do this, write out the factors you would multiply together to get the monomial, including the variable.
   
   For more information on how to factor, read Factor a Number.
   
   Rewrite the expression using the factors in the numerator and the denominator.
   
   For example, 4x{\displaystyle 4x} would factor as 2×2×x{\displaystyle 2\times 2\times x} and 16x2{\displaystyle 16x^{2}} would factor as 2×2×2×2×x×x{\displaystyle 2\times 2\times 2\times 2\times x\times x}.
   
   So, factored out, your expression will look like this: 2×2×x2×2×2×2×x×x{\displaystyle {\frac {2\times 2\times x}{2\times 2\times 2\times 2\times x\times x}}} , To do this, cross out factors in the numerator and denominator that match.
   
   These cancel out because you are dividing a factor by itself, which equals
   1.For example, you can cross out two 2s and one x in the numerator and the denominator:2×2×x2×2×2×2×x×x{\displaystyle {\frac {{\cancel {2}}\times {\cancel {2}}\times {\cancel {x}}}{{\cancel {2}}\times {\cancel {2}}\times 2\times 2\times {\cancel {x}}\times x}}} , Remember that terms cancel to
   1.
   
   So if you have canceled all the terms in the numerator or denominator, you will still be left with
   1.
   
   For example:2×2×x2×2×2×2×x×x{\displaystyle {\frac {{\cancel {2}}\times {\cancel {2}}\times {\cancel {x}}}{{\cancel {2}}\times {\cancel {2}}\times 2\times 2\times {\cancel {x}}\times x}}}12×2×x{\displaystyle {\frac {1}{2\times 2\times x}}} , This will give you your final, simplified rational expression.
   
   For example:12×2×x{\displaystyle {\frac {1}{2\times 2\times x}}}14x{\displaystyle {\frac {1}{4x}}}
3. 3

   Step 3: Cancel out shared factors.

4. 4

   Step 4: Rewrite the expression with the remaining factors.

5. 5

   Step 5: Complete any multiplication in numerator or denominator.

Detailed Guide

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