1. ## Simplify

how do you simplify this

and make C the subject

thanks

2. Hello Turbo,

Simplify: $\displaystyle (3x)\left(\frac{10y^3x}{5y^3}-x\right)+\left(\frac{12x^4y^2}{3x^4y}-2y\right)(2y)$

$\displaystyle 3x(2x-x)+(4y-2y)(2y)$

$\displaystyle 3x(x)+2y(2y)$

$\displaystyle \boxed{3x^2+4y^2}$

Solve for C:

$\displaystyle Q=\frac{1}{R}\sqrt{\frac{L}{C}}$

$\displaystyle RQ=\sqrt{\frac{L}{C}}$

$\displaystyle (RQ)^2=\frac{L}{C}$

$\displaystyle C(RQ)^2=L$

$\displaystyle \boxed{C=\frac{L}{(RQ)^2}}$

3. thanks alot

4. ## hi

Hi there

I donŽt know what level youŽre at, so I donŽt know how much I should take
for granted that you know.
Can you see the "most obvious" simplifications you make?
Like shorten out the $\displaystyle y^3$ terms in the first fraction?

When you have factors like this for exampl: $\displaystyle \frac{10x^3y^2}{5x^3y}$
You see that the number ten is actually composed by two prime numbers, namely 2 and 5.
$\displaystyle 2 \cdot 5 = 10$
In the same way, $\displaystyle x^3 = x \cdot x \cdot x$

So youŽll end up with(using my example):
$\displaystyle \frac{10x^3y^2}{5x^3y} = 2y$

5. just forgot to mention for the second one

calculate the value of capacitence C in farads