Simplify (5a)/(24cf^4)+a/(36bc^4f^3)

$\frac{5 a}{24 c f^{4}} + \frac{a}{36 b c^{4} f^{3}}$

To write $\frac{5 a}{24 c f^{4}}$ as a fraction with a common denominator, multiply by $\frac{3 b c^{3}}{3 b c^{3}}$ .

$\frac{5 a}{24 c f^{4}} \cdot \frac{3 b c^{3}}{3 b c^{3}} + \frac{a}{36 b c^{4} f^{3}}$

To write $\frac{a}{36 b c^{4} f^{3}}$ as a fraction with a common denominator, multiply by $\frac{2 f}{2 f}$ .

$\frac{5 a}{24 c f^{4}} \cdot \frac{3 b c^{3}}{3 b c^{3}} + \frac{a}{36 b c^{4} f^{3}} \cdot \frac{2 f}{2 f}$

Write each expression with a common denominator of $72 b c^{4} f^{4}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5 a}{24 c f^{4}}$ by $\frac{3 b c^{3}}{3 b c^{3}}$ .

$\frac{5 a (3 b c^{3})}{24 c f^{4} (3 b c^{3})} + \frac{a}{36 b c^{4} f^{3}} \cdot \frac{2 f}{2 f}$

Multiply $3$ by $24$ .

$\frac{5 a (3 b c^{3})}{72 c f^{4} (b c^{3})} + \frac{a}{36 b c^{4} f^{3}} \cdot \frac{2 f}{2 f}$

Raise $c$ to the power of $1$ .

$\frac{5 a (3 b c^{3})}{72 (c^{3} c^{1}) f^{4} b} + \frac{a}{36 b c^{4} f^{3}} \cdot \frac{2 f}{2 f}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{5 a (3 b c^{3})}{72 c^{3 + 1} f^{4} b} + \frac{a}{36 b c^{4} f^{3}} \cdot \frac{2 f}{2 f}$

Add $3$ and $1$ .

$\frac{5 a (3 b c^{3})}{72 c^{4} f^{4} b} + \frac{a}{36 b c^{4} f^{3}} \cdot \frac{2 f}{2 f}$

Multiply $\frac{a}{36 b c^{4} f^{3}}$ by $\frac{2 f}{2 f}$ .

$\frac{5 a (3 b c^{3})}{72 c^{4} f^{4} b} + \frac{a (2 f)}{36 b c^{4} f^{3} (2 f)}$

Multiply $2$ by $36$ .

$\frac{5 a (3 b c^{3})}{72 c^{4} f^{4} b} + \frac{a (2 f)}{72 b c^{4} f^{3} f}$

Raise $f$ to the power of $1$ .

$\frac{5 a (3 b c^{3})}{72 c^{4} f^{4} b} + \frac{a (2 f)}{72 b c^{4} (f^{1} f^{3})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{5 a (3 b c^{3})}{72 c^{4} f^{4} b} + \frac{a (2 f)}{72 b c^{4} f^{1 + 3}}$

Add $1$ and $3$ .

$\frac{5 a (3 b c^{3})}{72 c^{4} f^{4} b} + \frac{a (2 f)}{72 b c^{4} f^{4}}$

Reorder the factors of $72 b c^{4} f^{4}$ .

$\frac{5 a (3 b c^{3})}{72 c^{4} f^{4} b} + \frac{a (2 f)}{72 c^{4} f^{4} b}$

Combine the numerators over the common denominator.

$\frac{5 a (3 b c^{3}) + a (2 f)}{72 c^{4} f^{4} b}$

Simplify the numerator.

Factor $a$ out of $5 a \cdot 3 b c^{3} + a \cdot 2 f$ .

Factor $a$ out of $5 a \cdot 3 b c^{3}$ .

$\frac{a (5 \cdot 3 b c^{3}) + a \cdot 2 f}{72 c^{4} f^{4} b}$

Factor $a$ out of $a \cdot 2 f$ .

$\frac{a (5 \cdot 3 b c^{3}) + a (2 f)}{72 c^{4} f^{4} b}$

Factor $a$ out of $a (5 \cdot 3 b c^{3}) + a (2 f)$ .

$\frac{a (5 \cdot 3 b c^{3} + 2 f)}{72 c^{4} f^{4} b}$

Multiply $5$ by $3$ .

$\frac{a (15 b c^{3} + 2 f)}{72 c^{4} f^{4} b}$