ADDING AND SUBTRACTING RATIONAL EXPRESSIONS EXAMPLE PROBLEMS

Problem 1 :

25x2+5x-43x+3

Solution:

25x2+5x-43x+35x2+5x=5x(x+1)3x+3=3(x+1)LCM=15x(x+1)=25x(x+1)×33-43(x+1)×5x5x=2×3-4(5x)15x(x+1)=6-20x15x(x+1)

Problem 2 :

3a4a-20+9a6a-30

Solution:

3a4a-20+9a6a-304a-20=4(a-5)6a-30=6(a-5)LCM=24(a-5)=3a4(a-5)×66+9a6(a-5)×44=18a+36a24(a-5)=54a24(a-5)=9a4(a-5)

Problem 3 :

ty-t-yy+t

Solution:

ty-t-yy+tLCM=(y-t)(y+t)=ty-t×y+ty+t-yy+t×y-ty-t=t(y+t)-y(y-t)(y-t)(y+t)=ty+t2-y2+ty(y-t)(y+t)=t2+2ty-y2y2-t2

Problem 4 :

xx-5+x-5x

Solution:

xx-5+x-5xLCM=x(x-5)=xx-5×xx+x-5x×x-5x-5=x2+(x-5)(x-5)x(x-5)=x2+x2-10x+25x(x-5)=2x2-10x+25x(x-5)

Problem 5 :

xx2+5x+6-2x2+3x+2

Solution:

xx2+5x+6-2x2+3x+2x2+5x+6=(x+2)(x+3)x2+3x+2=(x+1)(x+2)=x(x+2)(x+3)-2(x+1)(x+2)LCM=(x+1)(x+2)(x+3)=x(x+2)(x+3)×x+1x+1-2(x+1)(x+2)×x+3x+3=x(x+1)-2(x+3)(x+1)(x+2)(x+3)=x2+x-2x-6(x+1)(x+2)(x+3)=x2-x-6(x+1)(x+2)(x+3)=(x+2)(x-3)(x+1)(x+2)(x+3)=x-3(x+1)(x+3)

Problem 6 :

2xx2-1-3x2+5x+4

Solution:

2xx2-1-3x2+5x+4x2-1=(x+1)(x-1)x2+5x+4=(x+1)(x+4)=2x(x+1)(x-1)-3(x+1)(x+4)LCM=(x-1)(x+1)(x+4)=2x(x+1)(x-1)×x+4x+4-3(x+1)(x+4)×x-1x-1=2x(x+4)-3(x-1)(x-1)(x+1)(x+4)=2x2+8x-3x+3(x-1)(x+1)(x+4)=2x2+5x+3(x-1)(x+1)(x+4)=(2x+3)(x+1)(x-1)(x+1)(x+4)=2x+3(x-1)(x+4)

Problem 7 :

xx2+15x+56-7x2+13x+42

Solution:

xx2+15x+56-7x2+13x+42x2+15x+56=(x+7)(x+8)x2+13x+42=(x+6)(x+7)=x(x+7)(x+8)-7(x+6)(x+7)LCM=(x+6)(x+7)(x+8)=x(x+7)(x+8)×x+6x+6-7(x+6)(x+7)×x+8x+8=x(x+6)-7(x+8)(x+6)(x+7)(x+8)=x2+6x-7x-56(x+6)(x+7)(x+8)=x2-x-56(x+6)(x+7)(x+8)=(x+7)(x-8)(x+6)(x+7)(x+8)=x-8(x+6)(x+8)

Problem 8 :

2xx2-9+5x2+x-6

Solution:

2xx2-9+5x2+x-6x2-9=(x+3)(x-3)x2+x-6=(x-2)(x+3)=2x(x+3)(x-3)+5(x-2)(x+3)LCM=(x-2)(x-3)(x+3)=2x(x+3)(x-3)×x-2x-2+5(x-2)(x+3)×x-3x-3=2x(x-2)+5(x-3)(x-2)(x-3)(x+3)=2x2-4x+5x-15(x-2)(x-3)(x+3)=2x2+x-15(x-2)(x-3)(x+3)=(x+3)(2x-5)(x-2)(x-3)(x+3)=2x-5(x-2)(x-3)

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