SOLVING RATIONAL EQUATIONS PRACTICE
Solve each equation. Remember to check for extraneous solutions.
Problem 1 :
Solution:
Problem 2 :
Solution:
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