The first step in solving this equation is to add the fractions, giving us: 

$\displaystyle \frac{2}{3}x=\frac{7}{15}$

To solve for $\displaystyle x$, we need to divide both sides by $\displaystyle \frac{2}{3}$.

Remember: When we divide a number by a fraction, we "switch" (find the reciprocal) of the fraction and mulitply it to the number.

$\displaystyle \bigg(\frac{3}{2}\bigg)\bigg(\frac{2}{3}\bigg)x=\bigg(\frac{7}{15}\bigg) \bigg(\frac{3}{2}\bigg)$

The right side of the equation cancels out leaving $\displaystyle x$ alone: 

$\displaystyle x=\frac{7\times 3}{15\times 2}=\frac{21}{30}$

Notice: Both the numerator and denominator are divisble by $\displaystyle 3$ so we can simplify this further.

$\displaystyle x=\frac{7}{10}$

The problem can be made easier by first simplifying each fraction: $\displaystyle \frac{3}{6}=\frac{1}{2}$ and $\displaystyle \frac{12}{4}=\frac{3}{1}$. 

This brings our new problem to $\displaystyle \frac{1}{2}\cdot\frac{3}{1}$.

Now, the numerators are multiplied by each other then the denomenators are multiplied by each other: $\displaystyle \frac{1\cdot3}{2\cdot1}=\frac{3}{2}$.

To solve, we must turn the division problem into a multiplication problem by "flipping" the second fraction (dividing by a fraction is the same as multiplying by its reciprocal):

 $\displaystyle \frac{5}{3}\div\frac{7}{6}=\frac{5}{3}\cdot\frac{6}{7}$.

Then, we multiply the numerators followed by the denomenators:

 $\displaystyle \frac{5\cdot6}{3\cdot7}=\frac{30}{21}$.

Lastly, the fraction must be simplified by a factor of 3: 

$\displaystyle \frac{30}{21}=\frac{10}{7}$, which gives us our final answer. 

To multiply fractions, just multiply the numerators, then the denominators, and then simplify.

$\displaystyle (\frac{x^2}{z})(\frac{x^2z^2}{y})=\frac{x^4z^2}{zy}=\frac{x^4z}{y}$

To multiply fractions, multiply the numerators and denominators together, then simplify.

$\displaystyle (\frac{ab^2c}{a^{\frac{1}{2}}b^4c^3})(\frac{abc^2}{c})=\frac{a^2b^3c^3}{a^{\frac{1}{2}}b^4c^4}=\frac{a^{\frac{3}{2}}}{bc}$

Multiply the numerators and denominators. Then, simplify.

$\displaystyle (\frac{4}{5}x)(\frac{6}{13}y)=(\frac{4x}{5})(\frac{6y}{13})=\frac{24xy}{65}$

Multiply the numerators and denominators, then simplify.

$\displaystyle (\frac{15}{7x})(\frac{12x^2}{5})=\frac{180x^2}{35x}=\frac{36}{7}x$

In order to divide fractions, you need to multiply the first fraction by the reciprocal of the second one.

$\displaystyle \frac{36x^2y}{5x^5y^{-2}}\div\frac{9x^{-3}}{25}=\frac{36x^2y}{5x^5y^{-2}}\times\frac{25}{9x^{-3}}$

Now, multiply the numerators and denominators together, then simplify.

$\displaystyle \frac{36x^2y}{5x^5y^{-2}}\times\frac{25}{9x^{-3}}=\frac{900x^2y}{45x^2y^{-2}}=20y^3$

To divid fractions, you need to multiply the first fraction by the reciprocal of the second.

$\displaystyle (\frac{25st^2}{6s^3t^5})\div(\frac{30s^{-9}}{45s^2t^7})=(\frac{25st^2}{6s^3t^5})\times(\frac{45s^2t^7}{30s^{-9}})$

Now, multiply the numerators and denominators together, then simplify.

$\displaystyle (\frac{25st^2}{6s^3t^5})\times(\frac{45s^2t^7}{30s^{-9}})=\frac{1125s^3t^9}{180s^{-6}t^5}=\frac{25s^9t^4}{4}$

To divide fractions, you need to multiply the first fraction by the reciprocal of the second.

$\displaystyle (\frac{12m^2n}{16m^3n^4})\div(\frac{8m^{-4}n}{18m^4n^2})=(\frac{12m^2n}{16m^3n^4})\times(\frac{18m^4n^2}{8m^{-4}n})$

Now, multiply the numerators and denominators, then simplify.

$\displaystyle (\frac{12m^2n}{16m^3n^4})\times(\frac{18m^4n^2}{8m^{-4}n})=\frac{216m^6n^3}{128m^{-1}n^5}=\frac{27m^7}{16n^2}$