Question

I have a rational expression to simplify, but needs help. Can you help?

Answer 1

Yes we can.

Answer 2

Although, i'm afraid we're going to need to see the expression first.

Answer 3

I cant write it out but i will try to explain, it is 9y square plus 3y minus 2 over 12 y square plus 5 y minus 2 divided by 9y square minus 6y plus 1 over 8y square minus 10y minus 3.

Answer 4

9y^2 + 3y - 2
-------------
12y^2 + 5y - 2
------------------
9y^2 - 6y + 1
------------
8y^2 - 10y - 3 ?????

Answer 5

That is correct, can I see how you work it out?

Answer 6

Does that question mark means that you dont know or what?

Answer 7

just wanted to confirm that i got the question right or not....

Answer 8

ok, it is correct

Answer 9

we treat like a question of fractions and as a first step we change the operation from divide to multiply by flipping over the second one as follows

9y^2 + 3y - 2
-------------
12y^2 + 5y - 2
------------------
9y^2 - 6y + 1
------------
8y^2 - 10y - 3


9y^2 + 3y - 2 8y^2 - 10y - 3
------------- * --------------
12y^2 + 5y - 2 9y^2 - 6y + 1

Answer 10

@Harkirat....never gave up from writing so much huh? :P

Answer 11

@angela210793

what is the fun in just giving the ans........the asker still does not know how to solve it !!☺

Answer 12

☺☺

Answer 13

Ok I understand up to that point but can I cancel anything from there?

Answer 14

now factorise all the four quadratic polynomials....

9y^2 + 3y - 2 = 9y^2 +6y -3y -2 = 3y(3y + 2) -1(3y + 2) = (3y - 1)(3y + 2)

12y^2 + 5y - 2 = 12y^2 +8y -3y -2 = 4y(3y + 2) -1(3y + 2) = (4y - 1)(3y + 2)

8y^2 - 10y - 3 = 8y^2 -12y + 2y - 3 = 4y(2y - 3) +1(2y - 3) = (4y + 1)(2y - 3)

9y^2 - 6y + 1 = 9y^2 -3y -3y + 1 = 3y(3y - 1) -1(3y -1) = (3y - 1)(3y - 1)

Answer 15

be patient, typing takes time....

Answer 16

perfect I understand so far

Answer 17

9y^2 + 3y - 2 8y^2 - 10y - 3
------------- * --------------
12y^2 + 5y - 2 9y^2 - 6y + 1


(3y - 1)(3y + 2) (4y + 1)(2y - 3)
= --------------- * ---------------
(4y - 1)(3y + 2) (3y - 1)(3y - 1)

Now combine and rearrange the numerator and denominator as follows


(2y - 3) * (3y - 1) * (3y + 2) * (4y + 1)
= ---------------------------------
(3y - 1) * (3y - 1) * (3y + 2) * (4y - 1)

Now cancelling out common factors from Num and Denom


(2y - 3) * (4y + 1)
= ----------------
(3y - 1) * (4y - 1)

Answer 18

No common factors left, so now just carry out the multiplication......

(2y - 3) * (4y + 1)
= ----------------
(3y - 1) * (4y - 1)

8y^2 + 2y - 12y - 3 8y^2 - 10y - 3
= ------------------ = --------------
12y^2 - 3y - 4y + 1 12y^2 - 7y + 1

Answer 19

Is the whole process clear????

Answer 20

ok I got it, you are a brainer, now what is the domain of the answer?

Answer 21

sorry, this part someone else will hv to answer as I am not too sure about the domain thing.....

Answer 22

Ok you are a great tutor. I am a 49 year old father who left hight school in 1981. I have one more can you help

Answer 23

Don't worry, we r both about the same age..... ( I was born in 1963 )

go ahead, ask the next one.......

Answer 24

x square plus x minus 6 over x square plus 4x minu 5 times x square minus 25 over x square plus 2x minus 15

Answer 25

Did you get it?

Answer 26

Sorry, I was attending another query....

Answer 27

x^2 + x - 6 5x^2 - 25
------------ - --------------
x^2 + 4x x^2 + 2x - 15

Have I written this correct ????

Answer 28

no let me repeat it x square plus x minus 6 over x square plus 4x minus 5 multipy by x square minus 25 over x square plus 2x minus 15

Answer 29

x^2 + x - 6
-----------------------
( x^2 + 4x) - (5x^2 - 25)
---------------------------
x^2 + 2x - 15

????

Answer 30

It wud be easier if u write it like I hv done.......

Answer 31

ok let me try
x^2 + x - 6 x^2 - 25
-------------X ----------
x^2 + 4x - 5 x^2 + 2x - 15

Answer 32

ok.... good.......

Answer 33

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

x^2 + 4x - 5 = x^2 + 5x - x - 5 = x(x + 5) -1(x + 5) = (x - 1)(x + 5)

x^2 - 25 = (x)^2 - (5)^2 = (x + 5)(x - 5)

x^2 + 2x - 15 = x^2 + 5x - 3x - 15 = x(x + 5) -3(x + 5) = (x - 3)(x + 5)

Answer 34

ok I got the factoring part right.

Answer 35

x^2 + x - 6 x^2 - 25
------------- X --------------
x^2 + 4x - 5 x^2 + 2x - 15

(x - 2)(x + 3) (x + 5)(x - 5)
= -------------- x --------------
(x - 1)(x + 5) (x - 3)(x + 5)


(x - 2) * (x + 3) * (x + 5) * (x - 5)
= --------------------------------
(x - 1) * (x - 3) * (x + 5) * (x + 5)


(x - 2) * (x + 3) * (x - 5)
= ------------------------
(x - 1) * (x - 3) * (x + 5)

Answer 36

Now can u carry out the multiplication to get the final answer.....

Answer 37

(x - 2) * (x + 3) * (x - 5) (x^2 + 3x - 2x - 6)(x - 5)
= ------------------------ = -----------------------
(x - 1) * (x - 3) * (x + 5) (x^2 - 3x - x + 3)(x + 5)


(x^2 + x - 6)(x - 5) x^3 + x^2 - 6x - 5x^2 - 5x + 30
= -------------------- = --------------------------------
(x^2 - 4x + 3)(x + 5) x^3 - 4x^2 + 3x + 5x^2 - 20x + 15


x^3 - 4x^2 - 11x + 30
= -----------------------
x^3 + x^2 - 17x + 15

Answer 38

ok thank you, I need to study this one some more, I got lost at the end. Thanks any way