This topic can be tricky, and if you don't already know how to add and subtract normal fractions, I highly recommend that you do that before moving on to algebraic fractions. Right, let's say we're given this question:
Calculate x - 2 / 3 + 2x + 3 / 4
To add fractions, they need a common denominator, and the easiest way to do that is to multiply the denominators together:
3 x 4 = 12
So we should make both denominators 12. But now we have to change the numerators too - we multiply them by the same thing we multiplied the denominators by. For example, for the first fraction, we multiply 3 by 4 to get 12, so we need to multiply x + 2 by 4 as well:
(x + 2) x 4 = 4(x + 2)
We don't need to expand this until we're combining the 2 fractions.
So this means fraction 1 is now:
4(x + 2)
12
Now for fraction 2. We multiplied 4 by 3 to get 12, so we need to multiply 2x + 3 by 3 too:
(2x + 3) x 3 = 3(2x + 3)
Fraction 2 is now:
3(2x + 3)
12
Now that both fractions have the same denominator, we just need to add their numerators:
3(2x + 3) + 4(x - 2)
12
If we expand the brackets (please see that topic!) we get:
6x + 9 + 4x - 8
12
Simplifying, this makes;
10x - 1
12
And thjat's our answer! Feel free to use our quiz to test your knowledge on this:
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