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Algebraic fractions. Please help

I have homework about algebraic fractions and im stuck on three questions i tried doing them a couple of times but i cant seem to get the answer right.

Show that each algebraic fraction simplifies to the given expression:

3 | 4
------ - ------- = 2 Show that it simplifies to 8x(squared)+31x+2=0
4x+1 x+2

2 | 6
-------- - -------- = 11 Show that it simplifies to 22x(squared) +21x-19=0
2x-1 x+1

. 3 |4
-------- - -------- = 1 Show that it simplifies to x(squared)-x=0
2x-1 3x-1
(edited 7 years ago)
Original post by Anonymous1502
I have homework about algebraic fractions and im stuck on three questions i tried doing them a couple of times but i cant seem to get the answer right.

Show that each algebraic fraction simplifies to the given expression:

3 | 4
------ - ------- = 2 Show that it simplifies to 8x(squared)+31x+2=0
4x+1 x+2


Post your working for the first one, say, and lets see what's happening.
Original post by ghostwalker
Post your working for the first one, say, and lets see what's happening.


For the first one i did:

3(x+2)-4(4x+1)
---------------------
(4x+1)(x+2)
3x+6-16x-4= - 13x+10

-13x+10
---------- =2
(4x+1)(x+2)

then i multiplied the bottom

-13x+10=2(4x+1)(x+2)

=2(4x squared + 8x+ x+2
=4x squared +9x+2

* 2

8x squared +18x+4= -13x+10

then i took away 10 and added 13x
= 8x squared +31x-6=0

so i dont know why it does not equal 8x squared +31x+2=0
Original post by Anonymous1502
For the first one i did:

3(x+2)-4(4x+1)
---------------------
(4x+1)(x+2)
3x+6-16x-4= - 13x+10

-13x+10
---------- =2
(4x+1)(x+2)



6 - 4 does not equal 10

Just an arithmetic slip.
Original post by ghostwalker
6 - 4 does not equal 10

Just an arithmetic slip.


How would you do the other questions for the the 2nd one i got:

2(x+1)-6(2x-1)
------------------- =11
(2x-1)(x+1)

2x+2-12x+6=

-10x-4
-----------
(2x-1)(x+1)

-10x-4=11(2x-1)(x+1)

=11(2x squared +x-1)
-10x-4=22x squared +11x-11

then i added 10x and 4

0= 22x squared+21x-7

but this does not equal 22x squared+21x - 19=0
Original post by Anonymous1502
How would you do the other questions for the the 2nd one i got:

2(x+1)-6(2x-1)
------------------- =11
(2x-1)(x+1)

2x+2-12x+6=

-10x-4
-----------
(2x-1)(x+1)

-10x-4=11(2x-1)(x+1)

=11(2x squared +x-1)
-10x-4=22x squared +11x-11

then i added 10x and 4

0= 22x squared+21x-7

but this does not equal 22x squared+21x - 19=0


Same mistake. 2+6 is not -4.
Original post by ghostwalker
6 - 4 does not equal 10

Just an arithmetic slip.


but doesent +6 - - 4 equal a positive (10)
Original post by Anonymous1502
but doesent +6 - - 4 equal a positive (10)


Yeah it is, but that's not the operation you are doing. You have 3(2)-4(1)=6-4.

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