# Thread: Reducing to lowest terms(rational expression)

1. ## Reducing to lowest terms(rational expression)

Hello I'm new here, and can you help me with this problem.

I will be reporting these rational expression tommorow but I have limited time, I'm busy at all my other homeworks and I am trying to complete my science investigatory project today so please help me?

Here are the expressions:

( ONE )

a^2 + 4ab + 4b^2
------------------
a^2 - 4b^2
__________________________________________________ ____________________
( TWO )

9x^2 + 6xy + y^2
------------------
9x^2 - y^2

__________________________________________________ ____________________
( THREE )

4a + 4
------------------
a^2 + 2a + 1

__________________________________________________ ____________________
( FOUR )

6x + 12
------------------
x^2 + 4x + 4

__________________________________________________ ____________________
( FIVE )

6x^2 - 6
------------------
(x-1)^2

__________________________________________________ ____________________
( SIX )

5x^2 - 20
------------------
2x - 4

__________________________________________________ ____________________
( SEVEN )

x^2 - 16
------------------
2x + 8

__________________________________________________ ____________________
( EIGHT )

x^2 - 2x -3
------------------
x^2 - 9

__________________________________________________ ____________________
( NINE )

x^2 - 5x + 4
------------------
x^2 - 1
__________________________________________________ ____________________
( TEN )

2x^2 + x - 6
------------------
x^2 + x - 2

note: the symbol (^) denots that the no. on the right side of it is raised.

Thank you to everyone who can help

Welcome aboard!

These are all of the same type.
You are expected to know how to factor and reduce.
I'll do a few to get you started . . .

. . . a² + 4ab + 4b²
1) . ------------------
. . . . . a² - 4b²

. . . . . . .(a + 2b)(a + 2b)
Factor: . --------------------
. . . . . . .(a - 2b)(a + 2b)

. . . . . . . a + 2b
Reduce: . --------
. . . . . . . a - 2b

. . . . . 4a + 4
3) . --------------
. . . a² + 2a + 1

. . . . . . . . .4(a + 1)
Factor: . -----------------
. . . . . . .(a + 1)(a + 1)

. . . . . . . . .4
Reduce: . -------
. . . . . . . .a + 1

. . . 5x² - 20
6) . -----------
. . . . 2x - 4

. . . . . . .5(x² - 4) . . . . 5(x - 2)(x + 2)
Factor: . ----------- . = . -----------------
. . . . . . .2(x - 2) . . . . . . . 2(x - 2)

. . . . . . . 5(x + 2)
Reduce: . ----------
. . . . . . . . . .2

3. I will do the rest that Soroban didn't do.

2)

9x^2 + 6xy + y^2
------------------ =
9x^2 - y^2

(3x+y)(3x+y)
------------ =
(3x-y)(3x+y)

3x+y
----
3x-y

4)
6x + 12
--------------- =
x^2 + 4x + 4

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

6
----
x+2

5)

6x^2 - 6
---------- =
(x-1)^2

6(x^2 - 1)
--------- =
(x-1)(x-1)

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

6(x+1)
------
x-1

7)

x^2 - 16
----------- =
2x + 8

(x-4)(x+4)
---------- =
2(x+4)

x-4
---
2

8)

x^2 - 2x -3
------------- =
x^2 - 9

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

x+1
---
x+3

9)
x^2 - 5x + 4
-------------- =
x^2 - 1

(x-1)(x-4)
---------- =
(x-1)(x+1)

x-4
---
x+1

10)
2x^2 + x - 6
------------- =
x^2 + x - 2

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

2x-3
----
x-1

4. thank you thank you thank you!

thanks for the help