Fractions in Algebra
We can add, subtract, multiply and divide fractions in algebra in the same way we do in simple arithmetic.
To add fractions there is a simple rule:
(See why this works on the Common Denominator page).
x2 + y5 = (x)(5) + (2)(y)(2)(5)
x + 43 + x − 34 = (x+4)(4) + (3)(x−3)(3)(4)
= 4x+16 + 3x−912
Subtracting fractions is very similar, except that the + is now −
x + 2x − xx − 2 = (x+2)(x−2) − (x)(x)x(x−2)
= (x2 − 22) − x2x2 − 2x
= −4x2 − 2x
Multiplying fractions is the easiest one of all, just multiply the tops together, and the bottoms together:
3xx−2 × x3 = (3x)(x)3(x−2)
To divide fractions, first "flip" the fraction we want to divide by, then use the same method as for multiplying:
3y2x+1 ÷ y2 = 3y2x+1 × 2y