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.

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