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

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

Answers (1)

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
\(\frac{2}{9c}\ +\ \frac{7}{15c^{3}}=\frac{10c^{2}\ +\ 21}{45c^{3}}\)
0

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