Eyes on Final Fantasy Forums > Reference > Study Hall > rational expressions

[Moon Rabbits]

Simplify.

(7y^2 / y^2 - 9) * (4y + 2 / 14y^2)

[Tavrobel]

Begin by distributing terms to both the numerator and the denominator. Since this is multiplication, there shouldn't be anything wrong with that.

(7y²)(4y) + (7y²)(2) / (4y²)(y²) - (4y²)(9)

Combine like terms, if applicable. Then simplify.

(28y³+14y²) / (4y⁴-36y²)

Since we have a Y squared in every term, remove them from the problem.

(28y+14) / (4y²-36)

Factor 14 from the top (optional step).

14*(2y+1) / (4y²-36)

Factor out 2 from both the top and the bottom.

7*(2y+1) / (2y²-18)

Optionally:
Factor out a 2 from the bottom. That leaves you with a difference of squares.

7(2y+1) / 2(y²-9)
7(2y+1) / 2(y+3)(y-3)

If you need to do something else with the problem, now would be the time to do so.

Math sucks. Your only hope is suicide.

[rubah]

It'd be a lot easier if you divided seven y squared by fourteen y squared at the onset, leaving you with a 2 in the denominator :]] Then you just have (2y-1)/(y-3)(y+3) don't you?

[Tavrobel]

Ohh . I misread it as 4y^2. Waah.

[crono_logical]

Originally Posted by Rubah Lapah ^

It'd be a lot easier if you divided seven y squared by fourteen y squared at the onset, leaving you with a 2 in the denominator :]] Then you just have (2y-1)/(y-3)(y+3) don't you?

Where'd the 2y-1 come from, rubah?

[o_O]

Yeah, Allie.

Here's the working for anyone that wants it:

(7y2 / y2 - 9) * (4y + 2 / 14y2)

= (7y2 / 14y2) * (4y + 2 / y2 - 9) Rearranging the terms into a more desirable order, by commutativity.

= (1 / 2) * (4y + 2 / y2 - 9) Reducing left multiplicand.

= (4y + 2 / 2y2 - 18) Multiplying multiplicands.

= (2y + 1 / y2 - 9) Reducing again.

= (2y + 1) / (y + 3)(y - 3) Factorising.
 

[blackmage_nuke]

If you take the 2 out of 4y+2 to get 2(2y+1) then use that 2 to multiply with the 7y^2 to get 14y^2 then that cancels out with the 14y^2 on the bottom and your left with what o_O said

edit: and put your brackets correctly. i guess most people assume you meant
(7y^2 / (y^2 - 9)) * ((4y + 2) / 14y^2)

But sometimes that wont be so obvious

[rubah]

Originally Posted by crono_logical ^

Originally Posted by Rubah Lapah ^

It'd be a lot easier if you divided seven y squared by fourteen y squared at the onset, leaving you with a 2 in the denominator :]] Then you just have (2y-1)/(y-3)(y+3) don't you?

Where'd the 2y-1 come from, rubah?

gosh, didn't you see the +2 right afterwards? I must have forgotten it 8)