HOW TO SOLVE RATIONAL EQUATIONS

To solve rational equations, we have to know operations on fractions.

  • To add or subtract two or more fractions, we should make the denominators same. If the denominators are not same, we have to take least common multiple and simplify.
  • By combining fractions on both sides separately, we will get only one fraction on both side of the equal sign.
  • Then doing cross multiplication, we can get rid of the fractions.
  • If is necessary, we have to use distributive property and combing the like terms, we can isolate x.

Problem 1 :

x8+x+22=-1

Solution:

x8+x+22=-1x8+4(x+2)8=-1x8+4x+88=-15x+88=-15x+8=-85x=-16x=-165

Problem 2 :

x+23+x-34=1

Solution:

x+23+x-34=1By cross multiplication, we get4(x+2)+3(x-3)12=14x+8+3x-9 12=17x-112=17x-1=127x=13x=137

Problem 3 :

2x-13-5x-66=-2

Solution:

2x-13-5x-66=-22(2x-1)6-5x-66=-24x-26-5x-66=-24x-2-5x+66=-2-x+46=-2-x+4=-12-x=-16x=16

Problem 4 :

x4=4-x+23

Solution:

x4=4-x+23x4=12-(x+2)3x4=12-x-23x4=10-x3By cross multiplication, we get3x=4(10-x)3x=40-4x7x=40x=407

Problem 5 :

2x-73-1=x-46

Solution:

2x-73-1=x-462(2x-7)6-1×66=x-464x-14-66=x-464x-20=x-43x=16x=163

Problem 6 :

x+13-x6=2x-32

Solution:

x+13-x6=2x-322(x+1)6-x6=3(2x-3)62x+2-x6=6x-96x+26=6x-96x+2=6x-96x-x=2+95x=11x=115

Problem 7 :

x5-2x-53=34

Solution:

x5-2x-53=343x-10x+2515=34-7x+2515=34By cross multiplication, we get4(-7x+25)=45-28x+100=45-28x=-55x=5528

Problem 8 :

x+13+x-26=x+412

Solution:

x+13+x-26=x+4124(x+1)12+2(x-2)12=x+4124x+4+2x-412=x+4126x=x+45x=4x=45

Problem 9 :

x-65-2x-110=x-12

Solution:

x-65-2x-110=x-122(x-6)10-2x-110=5(x-1)102x-12-2x+110=5x-510-11=5x-55x=-6x=-65

Problem 10 :

2x+14-1-4x2=3x+76

Solution:

2x+14-1-4x2=3x+762x+14-2(1-4x)4=3x+762x+14-2-8x4=3x+762x+1-2+8x4=3x+7610x-14=3x+76By cross multiplication, we get6(10x-1)=4(3x+7)60x-6=12x+2848x=34x=3448x=1724

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