Math Help with Rational Expressions!?

Question

I need help with these Qs. The method I use is to multiply the tops by the LCD then simplify. Don't know what I'm doing wrong so show work please!

1. 1/(u+4) + 1/(u-4) = 6/(u^2-16)

2. x/8 + 1/(x-2) = (x+2)/(2x-4)

3. 5y/(y+1) - y/(y+6) = 4

4. d/(d-2) = (d+3)/(d+2) - d/(d^2-4)

5. 6y/(2y +1) - 3/y = -1

6. 2 + 4/(b-1) = 4/(b^2-b)

Answer 1

1. 1/(u+4) + 1/(u-4) = 6/(u^2-16)

        =1/(u+4)+1/(u-4)

       =[1(u-4)+1(u+4)]/[(u+4)(u-4)]                               (u+4),(u-4) in LCM (u+4)(u-4)

       =[u-4+u+4]/[u^2-16]                                              (a+b)(a-b)=(a^2-b^2)

      =2u/(u^2-16)

Answer 2

3. 5y/(y+1) - y/(y+6) = 4

5y/(y+1)-y/(y+6)=4

[5y(y+6)-y(y+1)]/[(y+1)(y+6)]=4                                                    (y+1),(y+6) in LCM

(5(y^2)+30y)-(y^2+y)]/(y^2+6y+1y+6)=4

(5(y^2)+30y-y^2-y)/(y^2+7y+6)=4

both side multiflying in 'y^2 +7y+6'

[(5(y^2)+30y-y^2-y)/(y^2+7y+6)](y^2 +7y+6)=4(y^2 +7y+6)

[(4(y^2)+29y)]=[4(y^2)+28y+24]

each side adding -(4(y^2)+28y)

(4(y^2)+29y)-(4(y^2)+28y)=(4(y^2)+28y+24)-(4(y^2)+28y)

(4(y^2)+29y-4(y^2)-28y)=(4(y^2)+28y+24-4(y^2)-28y)

(y)=24

                   there fore y=24

Comments

The simplified expression .

Answer 3

5. 6y/(2y +1) - 3/y = -1

6y/(2y+1)-3/y=-1

[6y(y)-3(2y+1)]/[(2y+1)(y)]=-1                                    (2y+1),y in LCM

(6(y^2)-6y-3)/[(2y+1)(y)]=-1

each side multiflying '(2y+1)(y)'

{(6(y^2)-6y-3)/[(2y+1)(y)]}[(2y+1)(y)]=-1[(2y+1)(y)]

6(y^2)-6y-3=-(2(y^2)+y)

6(y^2)-6y-3+2(y^2)+y=0

8(y^2)-5y-3=0

8(y^2)-8y+3y-3=0                                   factor simplication

8y(y-1)+3(y-1)=0

(8y+3)(y-1)=0

8y+3=0  or   y-1=0

8y=-3     or    y=1

y=-3/8

    there fore y=-3/8 or 1

Comments

The simplified expression is .

Answer 4

6. 2 + 4/(b-1) = 4/(b^2-b)

2+4/(b-1)=4/(b^2-b)

[2(b-1)+4]/(b-1)=4/b(b-1)

each side multiflying 'b-1'

{[2(b-1)+4]/(b-1)}(b-1)=[4/b(b-1)]/(b-1)

2b-2+4=4/b

each side multiflying 'b'

(2b+2)b=(4/b)b

2(b^2)+2b=4

2(b^2)+2b-4=0

2(b^2)+4b-2b-4=0

2b(b+2)-2(b+2)=0

(2b-2)(b+2)=0

2b-2=0   or  b+2=0

2b=2    or   b=-2

b=2/2

b=1

 there fore b=1 or -2

Comments

The simplified expression is .

Answer 5

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Answer 6

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Answer 7

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