1. ## -Simplify Fractions-

1) I'm at a loss of what to do here.

2) Is this correct?

3) Is this in lowest terms? Aka, did I do this right.

4) Is this correct?

5) Absolutely no clue. I'm probably going to have to ask my teacher monday how to do this because I'm so lost.

2. 1) $\frac {3}{49z^3y}-\frac{1}{21z^2y}$
$\implies \frac {3(21z^2y)-49z^3y}{(21z^2y)(49z^3y)}$
$\implies \frac {63z^2y-49z^3y}{1029z^5y^2}$
$\implies \frac {9z^2y-7z^3y}{147z^5y^2}$
$\implies \frac {z^2(9y-7zy)}{147z^5y^2}$
$\implies \frac {y(9-7z)}{147z^3y^2}$
$\implies \frac {9-7z}{147z^3y}$

2) Correct.

3) Correct.

4) Correct.

5) $\frac{\frac{1}{x}+\frac{1}{y}}{\frac{x^2-y^2}{xy}}$
$\implies\frac{\frac{x+y}{xy}}{\frac{x^2-y^2}{xy}}$
$\implies\frac{x+y}{xy}\cdot\frac{xy}{x^2-y^2}$
$\implies\frac{x+y}{x^2-y^2}$
$
\implies\frac{1}{x-y}
$

3. Originally Posted by Sean12345
1) $\frac {3}{49z^3y}-\frac{1}{21z^2y}$
$\implies \frac {3(21z^2y)-49z^3y}{(21z^2y)(49z^3y)}$
$\implies \frac {63z^2y-49z^3y}{1029z^5y^2}$
$\implies \frac {9z^2y-7z^3y}{147z^5y^2}$
$\implies \frac {z^2(9y-7zy)}{147z^5y^2}$
$\implies \frac {y(9-7z)}{147z^3y^2}$
$\implies \frac {9-7z}{147z^3y}$

2) Correct.

3) Correct.

4) Correct.

5) $\frac{\frac{1}{x}+\frac{1}{y}}{\frac{x^2-y^2}{xy}}$
$\implies\frac{\frac{x+y}{xy}}{\frac{x^2-y^2}{xy}}$
$\implies\frac{x+y}{xy}\cdot\frac{xy}{x^2-y^2}$
$\implies\frac{x+y}{x^2-y^2}$
$
\implies\frac{1}{x-y}
$