Welcome :: Homework Help and Answers :: Mathskey.com
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,459 questions

17,854 answers

1,446 comments

806,712 users

Math Help with Rational Expressions!?

+1 vote
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)
asked Jan 8, 2013 in ALGEBRA 1 by johnkelly Apprentice

7 Answers

+1 vote
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)
answered Jan 8, 2013 by richardson Scholar
+1 vote
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
answered Jan 8, 2013 by richardson Scholar

The simplified expression image.

+1 vote
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
answered Jan 8, 2013 by richardson Scholar

The simplified expression is image.

+2 votes

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

answered Jan 8, 2013 by richardson Scholar

The simplified expression is image.

+1 vote
i don't know...
answered Jan 8, 2013 by dkinz Apprentice
0 votes

1) The expression is image.

image

image

image

2) The expression is .

3) The expression is .

4) The expression is image.

image

image

image

image

5) The expression is image.

image

image

image

image

6) The expression is image.

image

image

image

image

image

image

image

answered Jul 4, 2014 by joly Scholar
edited Jul 4, 2014 by joly
0 votes

1) The expression is image.

image

image

image

2) The expression is .

3) The expression is .

image

image

image

image

4) The expression is image.

image

image

image

image

5) The expression is image.

image

image

image

image

6) The expression is image.

image

image

image

image

image

image

image

 

answered Jul 4, 2014 by joly Scholar

Related questions

asked Nov 28, 2014 in PRECALCULUS by anonymous
asked Aug 16, 2017 in ALGEBRA 1 by anonymous
asked Aug 20, 2014 in ALGEBRA 1 by anonymous
asked Aug 7, 2014 in ALGEBRA 1 by anonymous
...