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Simplify.
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Q. Simplify.
- Find Common Denominator: We are given the expression . To add these fractions, we need a common denominator. The common denominator for and is .
- Rewrite Fractions: Now we will rewrite each fraction with the common denominator of . To do this, we multiply the numerator and denominator of each fraction by the necessary form of to get the common denominator without changing the value of the fractions.
- Add Numerators: Now that we have a common denominator, we can add the numerators.
- Rationalize Denominator: To simplify the expression further, we can rationalize the denominator by multiplying the numerator and the denominator by .
- Simplify Numerator: Now we simplify the numerator and the denominator.
- Factor Square Numbers: We can simplify and further by factoring out the square numbers.
- Substitute Simplified Forms: Now we substitute the simplified forms of and back into the expression.
- Check Further Simplification: We can now see if there is any further simplification possible. However, since and do not have a common factor with , and and cannot be simplified further, this is the simplest form of the expression.
