SOLUTION: can you pleasee help me!!!!!!!!!! simplify the following rational expressions. If it is already in simplest form, choose simplest form {{{x+5/4}}} / {{{(x^2+5x)}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: can you pleasee help me!!!!!!!!!! simplify the following rational expressions. If it is already in simplest form, choose simplest form {{{x+5/4}}} / {{{(x^2+5x)}}}      Log On


   

Question 190524: can you pleasee help me!!!!!!!!!!
simplify the following rational expressions. If it is already in simplest form, choose simplest form
x%2B5%2F4 / %28x%5E2%2B5x%29
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Is the expression %28x%2B5%2F4%29%2F%28x%5E2%2B5x%29???


If so, then...


%28x%2B5%2F4%29%2F%28x%5E2%2B5x%29 Start with the given expression


%284x%2Bcross%284%29%285%2Fcross%284%29%29%29%2F%284%2Ax%5E2%2B4%2A5x%29 Multiply EVERY term by the inner LCD 4 to clear out the inner fractions.


%284x%2B5%29%2F%284x%5E2%2B20x%29 Multiply and simplify



So %28x%2B5%2F4%29%2F%28x%5E2%2B5x%29 simplifies to %284x%2B5%29%2F%284x%5E2%2B20x%29


In short, %28x%2B5%2F4%29%2F%28x%5E2%2B5x%29=%284x%2B5%29%2F%284x%5E2%2B20x%29 where x%3C%3E-5 or x%3C%3E0


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OR...

Is the expression %28%28x%2B5%29%2F4%29%2F%28x%5E2%2B5x%29 ???


If so, then...




%28%28x%2B5%29%2F4%29%2F%28x%5E2%2B5x%29 Start with the given expression


%28%28x%2B5%29%2F4%29%2F%28%28x%5E2%2B5x%29%2F1%29 Rewrite x%5E2%2B5x as %28x%5E2%2B5x%29%2F1


%28%28x%2B5%29%2F4%29%281%2F%28x%5E2%2B5x%29%29 Multiply the first fraction by the reciprocal of the second fraction.


%28x%2B5%29%2F%284%28x%5E2%2B5x%29%29 Combine the fractions


%28x%2B5%29%2F%284x%28x%2B5%29%29 Factor the denominator


highlight%28%28x%2B5%29%29%2F%284x%2Ahighlight%28%28x%2B5%29%29%29 Highlight the common terms.


cross%28%28x%2B5%29%29%2F%284x%2Across%28%28x%2B5%29%29%29 Cancel out the common terms.


1%2F%284x%29 Simplify



So %28%28x%2B5%29%2F4%29%2F%28x%5E2%2B5x%29 simplifies to 1%2F%284x%29


In short, %28%28x%2B5%29%2F4%29%2F%28x%5E2%2B5x%29=1%2F%284x%29 where x%3C%3E-5 or x%3C%3E0