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ADDING AND SUBTRACTING RATIONAL EXPRESSIONS EXAMPLES

Problem 1 :

5x+3y2x2y-3x+4yxy2

Solution:

5x+3y2x2y-3x+4yxy2LCM=2x2y2=5x+3y2x2y×yy-3x+4yxy2×2x2x=y(5x+3y)-2x(3x+4y)2x2y2=5xy+3y2-6x2-8xy2x2y2=-3xy+3y2-6x22x2y2=3y2-3xy-6x22x2y2

Problem 2 :

2x-1+2x+1

Solution:

2x-1+2x+1LCM=(x-1)(x+1)=2x-1×x+1x+1+2x+1×x-1x-1=2(x+1)+2(x-1)(x-1)(x+1)=2x+2+2x-2(x-1)(x+1)=4xx2-1

Problem 3 :

2zz-1-3zz+1

Solution:

2zz-1-3zz+1LCM=(z-1)(z+1)=2zz-1×z+1z+1-3zz+1×z-1z-1=2z(z+1)-3z(z-1)(z-1)(z+1)=2z2+2z-3z2+3z(z-1)(z+1)=-z2+5zz2-1

Problem 4 :

2x-5+34x

Solution:

2x-5+34xLCM=4x(x-5)=2x-5×4x4x+34x×x-5x-5=2(4x)+3(x-5)4x(x-5)=8x+3x-154x(x-5)=11x-154x(x-5)

Problem 5 :

8x2-4-3x+2

Solution:

8x2-4-3x+2x2-4=(x+2)(x-2)=8(x+2)(x-2)-3x+2LCM=(x+2)(x-2)=8(x+2)(x-2)-3x+2×x-2x-2=8-3(x-2)(x+2)(x-2)=8-3x+6(x+2)(x-2)=14-3xx2-4

Problem 6 :

4xx2-25+xx+5

Solution:

4xx2-25+xx+5x2-25=(x+5)(x-5)=4x(x+5)(x-5)+xx+5LCM=(x+5)(x-5)=4x(x+5)(x-5)+xx+5×x-5x-5=4x+x(x-5)(x+5)(x-5)=4x+x2-5x(x+5)(x-5)=x2-xx2-25

Problem 7 :

tt-3-54t-12

Solution:

tt-3-54t-124t-12=4(t-3)=tt-3-54(t-3)LCM=4(t-3)=tt-3×44-54(t-3)=4t-54(t-3)

Problem 8 :

2x+3+4(x+3)2

Solution:

2x+3+4(x+3)2LCM=(x+3)2=2x+3×x+3x+3+4(x+3)2=2(x+3)+4(x+3)2=2x+6+4(x+3)2=2x+10(x+3)2
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