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We have provided numerous questions on Simplifying the Rational Expressions Involving Sum and Difference. Rational Expression Addition and Subtraction is similar to the Addition and Subtraction of Fractions. To help you better understand the concept we took few examples and given step by step explanation.
1. Simplify the Expression 1/(x-1)+2/(x-1)?
Solution:
Given Rational Expression is 1/(x-1)+2/(x-1)
Since the Denominators are the Same we need to simply add the numerators and keep the denominator unchanged.
= (1+2)/x-1
= 3/x-1
2. Simplify the Rational Expression 2/x+2 – (x-1)/2+x
Solution:
Given Rational Expression is 2/x+2 – (x-1)/2+x
As the Denominators are the same we can simply combine the numerators to get a simplified expression
= 2-(x-1)/(x+2)
= (2-x+1)/(x+2)
= (3-x)/(x+2)
3. Find the Sum of 5/x2+x/3x2+3x
Solution:
Given Rational Expression is 5/x2+x/(3x2+3x)
Since the Denominators are Unlike applying distributive property we get
= [5(3x2+3x)+x.x2]/x2.(3x2+3x)
= [15x2+15x+x3]/3x4+3x3
= (15x2+15x+x3)/(3x4+3x3)
4. Subtract 6/x-5(x-1)/4?
Solution:
= 6/x-5(x-1)/4
= 6/x- (5x+5)/4
= (6.4-x.(5x+5))/x.4
= (24-5x2-5x)/4x
5. Simplify the Expression
-3/4 + 5/3 – 7/2
Solution:
Since the Denominators aren’t the same find the LCM of Denominators and then simplify them
=(-3*3+5*4-7*6) /12
= (-9+20-42)/12
= -31/12
6. Simplify the following
5/3 + (-2)/4 – (-2)/8
Solution:
Since the Denominators aren’t the same find the LCM of Denominators and then simplify them
LCM of 3, 4, 8 is 24
= (5*8-2*6+2*3)/24
= (40-12+6)/24
= 34/24
= 17/12
7. What should be subtracted from (3/5 – 2/3) to get 1/6?
Solution:
From the given data
3/5-2/3-x = 1/6
3/5-2/3-1/6 = x
x =3/5-2/3-1/6
LCM of 5, 3, 6 is 30
= (3*6-2*10-1*5)/30
= (18-20-5)/30
= -7/30