Remember the Algebraic Fractions simplification:
y + y - 3
3 4
= 4 x y + 3 (y - 3). (Step 1 : Multiply each for same denominator (L.C.M))
4 x 3 + 3 x4
= 4y + 3y - 9 (Step2 : Combine into a single fraction)
12 (Step 3 : Simplify : Do Order of Operations)
= y - 9
12
<< L2 - NA/O>>
Linear denominator
Similarly, for algebraic expression with variable in the denominator, we simplify the expression accordingly. We can 'treat' the variable as a 'unique' number
Example
a. 2 - y - 3
y 4
= 2 - (x -3) (Step 1 : Multiply each to get same denominator)
4 x y 4 x y
= 2 - x + 3 (Step2 : Combine to 1 fractional term)
4y (Step 3 : Simplify, - x - = +)
= 5 - x
4y
Quadratics Denominator
Example
Simplify 3 + 2
y – 3 y
= 3 + 2 (Step1: Identify common factors)
y – 3 y (Common factor of y, (y – 3) = y x (y – 3))
= y x 3 + 2 x (y - 3) (Step2 : Combine to 1 fractional term)
y x (y – 3) y x(y – 3)
= 3y + 2 (y - 3)
y(y – 3)
= 3y + 2y - 6 (Step 3 : Simplify, - x - = +)
y(y – 3)
= 5y - 6
y(y – 3)
Example
Simplify 1 + 2
x – 3 (x – 3)2
= 1 + 2 (Step1: Identify common factors)
y – 3 (y – 3)2 (y – 3)(y – 3)=> (y – 3)2 = C.factor
= (x – 3) + 2 (Step2 : Combine to 1 fractional term)
(y – 3)(y – 3) (x – 3)2
Step3: Simplify
= x – 3 + 2
(x – 3)2
= x – 1
(x – 3)2
Practice
1. Simplify the following:
1 + 2
x - 2 x - 3
(b) 1 + 2
x2 - 9 x - 3
(c) 1 + 2
x - 2 (x - 2)2
2. Solve for x
(a) x + x - 3. = 6
3 4
b. 3 = 6
x – 4
