How to make this have a common denominator. This is hard-please help??

Question

This is the expression:

(((5a+5h)/(1+a²+2ah+h²)) - ((5a)/(1+a²)))/ h

I'm just not sure how to simplify the numerator because they don't share the same denominator..but i know that it can be simplified further..my problem is that i don't know what to multiply the two terms in the numerator by in order to make them have the same denominator.

Hopefully you can understand my question and please help!!

Thank you!!

Answer 1

(((5a+5h)/(1+a²+2ah+h²)) - ((5a)/(1+a²)))/ h

I'm just not sure how to simplify the numerator because they don't share the same denominator..but i know that it can be simplified further..my problem is that i don't know what to multiply the two terms in the numerator by in order to make them have the same denominator.

Ali M Just multiply the denominator of the complex term so you can not miss it. Then begin to simplify

Here it is

Your LCD = (1 + a² + 2ah + h²)(1 + a²) ← Least Common Denominator

=> (1 + a²)(5a + 5h)/LCD - (5a)(1 + a² + 2ah + h²)/LCD / h

=> 5a + 5h    + 5a³ + 5a²h   - 5a - 5a³ - 10a²h - 5ah²  / LCD x h

combining terms

=>  + 5h + 5a²h  - 10a²h - 5ah²  / LCD x h

=>  ( 5h + 5a²h  - 10a²h - 5ah² )h / LCD

=> 5h²(1 + a² - 2a² - ah) / LCD

=> 5h²(1 + a² - 2a² - ah) / (1 + a² + 2ah + h²)(1 + a²)

=> 5h²(1 + a² - 2a² - ah) / (1 + a² + 2ah + h²  + a² + a^4 + 2a³h + a²h² )

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Ans::=> 5h²(1 + a² - 2a² - ah) / (1 + 2a² + 2ah + h² + a^4 + 2a³h + a²h²   )

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This simplest form we can arrived

hope this helps

Answer 2

Multiply both of the denominators  from both fractions to the both the numerators. So that you cancell out the denominator, and mulitply the remaining numerator with the denominaotor of the other fraction.

and the the second fraction is also mulitplied by both denomintors of the two fractions, and cancell out leaving the other fractions denomintor to muliply with the remaining numerator.