# Worksheet on Rational Expressions Involving Sum and Difference | Rational Expressions Addition & Subtraction Worksheet

If you need help on Rational Expressions Involving Sum and Difference take the help of the Worksheets available. Have a glance at the Worksheet on Rational Expressions Involving Sum and Difference during your practice and take your preparation to the next level. Identify the knowledge gap and allot time to the areas you are lagging. For complete guidance make use of the Rational Numbers Worksheets and clear all your doubts related to them.

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