EXPRESSING TWO ALGEBRAIC FRACTIONS AS A SINGLE FRACTION

Adding and subtracting two or more fractions is also like adding or subtracting rational numbers.

Consider an example, express the following as single fraction.

2x+1+3x-2
single-fraction-q1

Using distributive property, do the possible simplification.

Write as a single fraction:

Problem 1 :

5x+1+7x+2

Solution:

=5x+1+7x+2=5(x+2)+7(x+1)(x+1) (x+2)=5x+10+7x+7(x+1) (x+2)=12x+17(x+1)(x+2)

Problem 2 :

2x+1+3x-2

Solution:

=2x+1+3x-2=2(x-2)+3(x+1)(x+1) (x-2)=2x-4+3x+3(x+1) (x-2)=5x-1(x+1)(x-2)

Problem 3 :

5x-1-4x+2

Solution:

=5x-1-4x+2=5(x+2)-4(x-1)(x-1) (x+2)=5x+10-4x+4(x-1) (x+2)=x+14(x-1)(x+2)

Problem 4 :

2x+2-42x+1

Solution:

=2x+2-42x+1=2(2x+1)-4(x+2)(x+2) (2x+1)=4x+2-4x-8(x+2) (2x+1)=-6(x+2)(2x+1)

Problem 5 :

3x-1+4x+4

Solution:

=3x-1+4x+4=3(x+4)+4(x-1)(x-1) (x+4)=3x+12+4x-4(x-1) (x+4)=7x+8(x-1)(x+4)

Problem 6 :

71-x-8x+2

Solution:

=71-x-8x+2=7(x+2)-8(1-x)(1-x) (x+2)=7x+14-8+8x(1-x) (x+2)=15x+6(1-x)(x+2)

Problem 7 :

1x+1+3x

Solution:

=1x+1+3x=x+3(x+1)x(x+1)=x+3x+3x(x+1)=4x+3x(x+1)

Problem 8 :

5x-2x+3

Solution:

=5x-2x+3=5(x+3)-2xx(x+3)=5x+15-2xx(x+3)=3x+15x(x+3)

Problem 9 :

xx+2+3x-4

Solution:

=xx+2+3x-4=x(x-4)+3(x+2)(x+2)(x-4)=x2-4x+3x+6(x+2)(x-4)=x2-x+6(x+2)(x-4)

Problem 10 :

2+4x-3

Solution:

=2+4x-3=2(x-3)+4x-3=2x-6+4x-3=2x-2x-3

Problem 11 :

3xx+2-1

Solution:

=3xx+2-1=3x-1(x+2)x+2=3x-x-2x+2=2x-2x+2

Problem 12 :

xx+3+x-1x+2

Solution:

=xx+3+x-1x+2=x(x+2)+(x+3)(x-1)(x+3)(x+2)=x2+2x+x2-x+3x-3(x+3)(x+2)=2x2+4x-3(x+3)(x+2)

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