maths help?

Question

how do u work out algebraic addition and subtraction of fractions if u dont know the value of the denominator? eg 2/y + 7/z =? can u tell me how? i know it has something to do with multiplying something....
ps i have a test 2moz so help asap will b much appreciated x]

Answer 1

Look for any common factors in the denominators first - these only need to be put in once.
Then put in any remaining factors from each denominator.

In your example, y and z have no common factors, so the denominator will just be yz. We are multiplying the first term by z/z and the second term by y/y, so we will get
2z/yz + 7y/yz = (2z+7y) / yz.

For a more complicated example, consider
(x+3) / (x^2-1) + (x+2) / (x^2-3x-2)
= (x+3) / [(x-1)(x+1)] + (x+2) / [(x-1)(x-2)]
Now (x-1) is a common factor of the two denominators, so we put this in once. We also need to put in (x+1) from the left and (x-2) from the right, so we get
= [(x+3)(x-2)] / [(x-1)(x+1)(x-2)] + [(x+2)(x+1)] / [(x-1)(x+1)(x-2)]
= [(x^2+x-6) + (x^2+3x+2)] / [(x-1)(x+1)(x-2)]
= (2x^2+4x-4) / [(x-1)(x+1)(x-2)]
= 2(x^2+2x-2) / [(x-1)(x+1)(x-2)]

If I was clever I'd have arranged this so that the top factorises into something that cancels out a factor of the denominator, but I didn't. ;-)

Answer 2

2/y + 7/z = (2z + 7y) / zy

If z and y have numerical values, then look for the higest common denominator. Else, the denominator becomes the product of the two.