# Thread: Help with rational expressions plz

1. ## 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:

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

2. 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

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

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 $\displaystyle c = -2$

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!

3. 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 $\displaystyle \sqrt{15}a^7b^3$

4. 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 $\displaystyle =a^7b^3\sqrt{35}$.