The value of addition of the rational expression \(\frac{2}{9c}\ +\ \frac{7}{15c^{3}}\ is\ \frac{10c^{2}\ +\ 21}{45c^{3}}\)

Given Information: The rational expression is \(\frac{2}{9c}\ +\ \frac{7}{15c^{3}},\)

Formula used:

Step1: factor the denominator.

Step2: multiply numerator and denominator of each expression by the factor missing from the denominators \(\frac{2}{9c}\ +\ \frac{7}{15c^{3}}\)

Step3: add the numerator and write the result over the common denominator.

Step4: the expression is already simplified

Calculation:

Consider the provided expression, \(\frac{2}{9c}\ +\ \frac{7}{15c^{3}}\)

Using Step 1 factor the denominator,

\(\frac{2}{9c}\ +\ \frac{7}{15c^{3}}=\frac{2}{3^{2}c}\ +\ \frac{7}{5\ \times\ 3c^{3}}\)

Now using step 2,

Multiply numerator and denominator of each expression by the factor missing from the denominators.

Therefore,

\(\frac{2}{9c}\ +\ \frac{7}{15c^{3}}=\frac{2\ \times\ (5c^{2})}{3^{2}c(5c^{2})}\ +\ \frac{7(3)}{5\ \times\ 3c^{3}(3)}\)

The above expression can be written as,

\(\frac{2}{9c}\ +\ \frac{7}{15c^{3}}=\frac{10c^{2}}{45c^{3}}\ +\ \frac{21}{45c^{3}}\)

Teast common denominator \(45c^{3}\) of the expression

\(\frac{2}{9c}\ +\ \frac{7}{15c^{3}}=\frac{10c^{2}}{45c^{3}}\ +\ \frac{21}{45c^{3}},\)

Therefore,

\(\frac{2}{9c}\ +\ \frac{7}{15c^{3}}=\frac{10c^{2}\ +\ 21}{45c^{3}}\)

Therefore, the value of addition of the rational expression

\(\frac{2}{9c}\ +\ \frac{7}{15c^{3}}=\frac{10c^{2}\ +\ 21}{45c^{3}}\)

Given Information: The rational expression is \(\frac{2}{9c}\ +\ \frac{7}{15c^{3}},\)

Formula used:

Step1: factor the denominator.

Step2: multiply numerator and denominator of each expression by the factor missing from the denominators \(\frac{2}{9c}\ +\ \frac{7}{15c^{3}}\)

Step3: add the numerator and write the result over the common denominator.

Step4: the expression is already simplified

Calculation:

Consider the provided expression, \(\frac{2}{9c}\ +\ \frac{7}{15c^{3}}\)

Using Step 1 factor the denominator,

\(\frac{2}{9c}\ +\ \frac{7}{15c^{3}}=\frac{2}{3^{2}c}\ +\ \frac{7}{5\ \times\ 3c^{3}}\)

Now using step 2,

Multiply numerator and denominator of each expression by the factor missing from the denominators.

Therefore,

\(\frac{2}{9c}\ +\ \frac{7}{15c^{3}}=\frac{2\ \times\ (5c^{2})}{3^{2}c(5c^{2})}\ +\ \frac{7(3)}{5\ \times\ 3c^{3}(3)}\)

The above expression can be written as,

\(\frac{2}{9c}\ +\ \frac{7}{15c^{3}}=\frac{10c^{2}}{45c^{3}}\ +\ \frac{21}{45c^{3}}\)

Teast common denominator \(45c^{3}\) of the expression

\(\frac{2}{9c}\ +\ \frac{7}{15c^{3}}=\frac{10c^{2}}{45c^{3}}\ +\ \frac{21}{45c^{3}},\)

Therefore,

\(\frac{2}{9c}\ +\ \frac{7}{15c^{3}}=\frac{10c^{2}\ +\ 21}{45c^{3}}\)

Therefore, the value of addition of the rational expression

\(\frac{2}{9c}\ +\ \frac{7}{15c^{3}}=\frac{10c^{2}\ +\ 21}{45c^{3}}\)