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How do you simplify #\frac { w + x } { w x ^ { 2} } + \frac { 7w + x } { w ^ { 2} x }#?

Answer 1

#((w^2 + 8xw + x^2))/(w^2x^2)#

To add fractions they must be over common denominators. In this case a common denominator would be #w^2x^2#. Therefore we need to multiply each fraction by the necessary form of #1# to provide this denominator:

#(w/w)(w + x)/(wx^2) + (x/x)(7w + x)/w^2x ->#

#(w(w + x))/(w^2x^2) + (x(7w + x))/(w^2x^2)#

We can now add the numerators and then expand and combine the terms within parenthesis. Or, expand the terms within parenthesis and then add and combine the common terms.

#((w(w + x)) + (x(7w + x)))/(w^2x^2)#

#((w^2 + wx) + (7xw + x^2))/(w^2x^2)#

#((w^2 + 8xw + x^2))/(w^2x^2)#

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Answer 2

Eli Assouline

To simplify the expression (\frac { w + x } { w x ^ { 2} } + \frac { 7w + x } { w ^ { 2} x }), first find a common denominator, which is (w^2x^2). Then combine the fractions and simplify. The simplified expression is (\frac{w^3 + 7w^2x + wx^2 + x^2}{w^2x^2}).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.