# Help with rational expressions plz

• Jul 19th 2009, 04:27 PM
ohiostatefan
Help with rational expressions plz
If anybody could help, I have a math exam tomorrow, and I'm working on the review...but I've been having alot of trouble. Usually I can figure this stuff out by studying my notes...but I'm at a loss. Any help would be appreciated. The first three are problems that I don't understand, the rest are ones that I've completed, but I'm not sure if they're right.

1. $\displaystyle x^2+x=20$

$\displaystyle 2x^2-5x=2$

3. Solve by completing the square:

$\displaystyle x^2+8x-9=0$

And the ones that I've completed, but not sure if they're right...I would appreciate if you could check these out.

1. $\displaystyle 6y \sqrt{27x^3y} - 3x \sqrt{12xy^3} + xy \sqrt{4xy}$

I got:

$\displaystyle 12xy \sqrt{3xy} + 2xy \sqrt{xy}$

2. $\displaystyle (4 \sqrt{x} + 3 \sqrt{y})(2 \sqrt{x} - 5 \sqrt{y})$

I got:

$\displaystyle 8x-14 \sqrt{xy} - 15y$

3. $\displaystyle \frac{\sqrt 75a^8b^5}{\sqrt 5ab^2}$

I got:

$\displaystyle b \sqrt{15a^7b}$
• Jul 19th 2009, 05:03 PM
pickslides
Quote:

Originally Posted by ohiostatefan
1. $\displaystyle x^2+x=20$

$\displaystyle x^2+x-20=0$

factors of 20 that add to give 1 are -4 & -5 so

$\displaystyle (x-4)(x+5)$

Quote:

Originally Posted by ohiostatefan

$\displaystyle 2x^2-5x=2$

$\displaystyle 2x^2-5x-2=0$

$\displaystyle x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$

in your case $\displaystyle a = 2, b= -5$ and $\displaystyle c = -2$

Quote:

Originally Posted by ohiostatefan

3. Solve by completing the square:

$\displaystyle x^2+8x-9=0$

$\displaystyle (x^2+8x+16)-9-16=0$

$\displaystyle (x+4)^2-9-16=0$

$\displaystyle (x+4)^2-25=0$

the square is now complete, now solve!
• Jul 19th 2009, 05:09 PM
pickslides
Quote:

Originally Posted by ohiostatefan
If
And the ones that I've completed, but not sure if they're right...I would appreciate if you could check these out.

1. $\displaystyle 6y \sqrt{27x^3y} - 3x \sqrt{12xy^3} + xy \sqrt{4xy}$

I got:

$\displaystyle 12xy \sqrt{3xy} + 2xy \sqrt{xy}$

2. $\displaystyle (4 \sqrt{x} + 3 \sqrt{y})(2 \sqrt{x} - 5 \sqrt{y})$

I got:

$\displaystyle 8x-14 \sqrt{xy} - 15y$

3. $\displaystyle \frac{\sqrt 75a^8b^5}{\sqrt 5ab^2}$

I got:

$\displaystyle b \sqrt{15a^7b}$

I agree with all your answers except the last problem, should be $\displaystyle \sqrt{15}a^7b^3$
• Jul 19th 2009, 05:29 PM
Stroodle
Would you not be required to express the answer in its simplest form?

i.e. $\displaystyle a^3 b\sqrt{15ab}$

Thanks :)

*edit - Actually is the question supposed to be $\displaystyle \frac{\sqrt{75}a^8b^5}{\sqrt{5}ab^2}$? Because then the answer would be $\displaystyle a^7b^3\sqrt{15}$. The above would be the answer to $\displaystyle \frac{\sqrt{75a^8b^5}}{\sqrt{5ab^2}}$. As it's written the question looks like $\displaystyle \frac{\sqrt{7}\times 5a^8b^5}{\sqrt{5}ab^2}$ which $\displaystyle =a^7b^3\sqrt{35}$.