# To calculate : The value of addition of the rational expression frac{2}{9c} + frac{7}{15c^{3}}

Question
To calculate : The value of addition of the rational expression $$\frac{2}{9c}\ +\ \frac{7}{15c^{3}}$$

2021-02-11
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
$$\frac{2}{9c}\ +\ \frac{7}{15c^{3}}=\frac{10c^{2}\ +\ 21}{45c^{3}}$$

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