How do you combine #a/(a-3)-5/(a+6)#?
To subtract these two fractions, as with any fractions, they need to be over common denominators. In this case the common denominator will be
Therefore, first we need to multiply each fraction by the correct form of
We can now expand the terms within parenthesis in each of the numerators:
We can now combine the fractions by subtracting the numerators and keeping the common denominator:
Now we can expand the terms within the parenthesis ensuring we keep the signs of the terms correct:
And then we can combine like terms in the numerator:
Or, is we want to expand the term in the denominator by cross multiplying we get: