factoring, simplifying, rational expressions, etc.

[michalie]

i have had much trouble trying to figure these few problems out. I need a LOT of help

if someone helps me out with this i will be forever greatful

sorry I can't figure out how to do exponents so everything in brackets is exponents

1) (x[3] - 2x[2]y + xy[2]) / (x[4] - x[2]y[2])

2) (x[-1]y[2] - x[2]y[-1]) / (x[-1] - y[-1])

this one some how I had the correct solution and wrong answer:

3) (t(t-4)) / 15 + 1/4

4) a pharmacist wishes to make 1.8 L of a 10% solution of boric acid by mixing 7.5% and 12 % solutions. How much of each type of solution should be used?

 

[tkhunny]

Re: test correction help! MUCHHHH NEEDED

x[3] - 2x[2]y + xy[2]
x[4] - x[2]y[2]

These appear to be straightforward factoring drills.

x^3 - 2(x^2)y + xy^2

There is an 'x' in each term.

x(x^2 - 2xy + y^2)

The part remaining in the parentheses should look familiar.

x(x-y)^2

use the rules you know. You do the next one.

 

[Denis]

Re: test correction help! MUCHHHH NEEDED

a pharmacist wishes to make 1.8 L of a 10% solution of boric acid by mixing 7.5% and 12 % solutions. How much of each type of solution should be used?

[7.5x + 12(1.8 - x)] / 1.8 = 10

x will be portion of 7.5% solution.

 

[soroban]

Re: test correction help! MUCHHHH NEEDED

Hello, michalie!

There's a "trick" for the second one . . .

\(\displaystyle \L2) \:\frac{x^{-1}y^2\,-\,x^2y^{-1}}{x^{-1}\,-\,y^{-1}}\)

Multiply top and bottom by \(\displaystyle xy:\)

. . \(\displaystyle \L\frac{xy}{xy}\,\cdot\,\frac{x^{-1}y^2\,-\,x^2y^{-1}}{x^{-1}\,-\,y^{-1}} \;=\;\frac{y^3\,-\,x^3}{y\,-\,x}\)

Factor: \(\displaystyle \L\:\frac{(y\,-\,x)(y^2\,+\,yx\,+\,x^2)}{(y\,-\,x)}\)\(\displaystyle \;=\;y^2\,+\,yx\,+\,x^2\)