SOLVING RATIONAL EQUATIONS PRACTICE

Solve each equation. Remember to check for extraneous solutions.

Problem 1 :

13n2+n+43n2=n+6n2

Solution:

13n2+n+43n2=n+6n21+n+43n2=3(n+6)3n21+n+4=3(n+6)5+n=3n+18n-3n=18-5-2n=13n=-132

Problem 2 :

12x2+13x=2x2

Solution:

12x2+13x=2x2Take LCM 2x2,3x=6x23+2x6x2=6×26x23+2x=122x=9x=92

Problem 3 :

53x2-56x=16x

Solution:

53x2-56x=16xTake LCM 3x2,6x=6x25×26x2-5x6x2=x6x210-5x=x10=x+5x6x=10x=106x=53

Problem 4 :

3v2=1v2+5v

Solution:

3v2=1v2+5v3v2=1v2+5vv23v2=1+5vv23=1+5v5v=2v=25

Problem 5 :

n2+n-62n2-n+52n=2n

Solution:

n2+n-62n2-n+52n=2nn2+n-62n2-n(n+5)2n2=2(2n)2n2n2+n-6-n2-5n=4n-4n-6=4n8n=-6n=-68n=-34

Problem 6 :

12=b-12b-b-26b2

Solution:

12=b-12b-b-26b2To take LCM of 2b,6b2=6b23b26b2=3b(b-1)-(b-2)6b23b2=3b2-3b-b+24b=2b=24b=12

Problem 7 :

p2-162p+12p=1

Solution:

p2-162p+12p=1p2-16+1=2pp2-2p-15=0(p-5) (p+3)=0p=5 or p=-3

Problem 8 :

a+3a+4-a2+7a+6a2+7a+12=1a2+7a+12

Solution:

a+3a+4-a2+7a+6a2+7a+12=1a2+7a+12 a+3a+4-(a+1)(a+6)(a+3)(a+4)=1(a+3)(a+4) (a+3)(a+3)(a+4)(a+3)-(a+1)(a+6)(a+3)(a+4)=1(a+3)(a+4) (a+3)(a+3)-(a+1)(a+6)=1a2+6a+9-a2-7a-6=1-a+3=1-a=-2a=2

Problem 9 :

a+2a+5=1a2+8a+15+1

Solution:

a+2a+5=1a2+8a+15+1a+2a+5=1(a+3)(a+5)+1(a+2)(a+3)(a+5)(a+3)=1(a+3)(a+5)+(a+3)(a+5)(a+3)(a+5)(a+2)(a+3)=1+(a+3)(a+5)a2+5a+6=1+a2+8a+15a2-a2+5a-8a+6-16=0-3a-10=0-3a=10a=-103

Problem 10 :

1-x2+x-30x2+4x=1x+4

Solution:

1-x2+x-30x2+4x=1x+41-(x-5)(x+6)x(x+4)=1x+4x(x+4)x(x+4)-(x-5)(x+6)x(x+4)=xx(x+4)x(x+4)-(x-5)(x+6)=xx2+4x-x2+5x-6x+30=x2x=-30x=-302x=-15

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