Question $\frac{\frac{4}{c}}{\frac{7}{c}+\frac{2}{c^{2}}}$

Studdy Solution

STEP 1

1. We need to simplify the given complex fraction.
2. The variable $c$ is non-zero to avoid division by zero.
3. The expression can be simplified by finding a common denominator.

STEP 2

1. Simplify the denominator of the complex fraction.
2. Simplify the entire complex fraction.

STEP 3

Identify the common denominator in the denominator of the complex fraction:
The denominator is $\frac{7}{c} + \frac{2}{c^2}$ .
The common denominator for $\frac{7}{c}$ and $\frac{2}{c^2}$ is $c^2$ .
Rewrite each term with the common denominator:
$\frac{7}{c} = \frac{7c}{c^2}$
$\frac{2}{c^2} = \frac{2}{c^2}$
Combine the terms:
$\frac{7c}{c^2} + \frac{2}{c^2} = \frac{7c + 2}{c^2}$

STEP 4

Simplify the entire complex fraction:
The original expression is:
$\frac{\frac{4}{c}}{\frac{7}{c} + \frac{2}{c^2}}$
Substitute the simplified denominator:
$\frac{\frac{4}{c}}{\frac{7c + 2}{c^2}}$
Simplify by multiplying by the reciprocal of the denominator:
$\frac{4}{c} \times \frac{c^2}{7c + 2}$
Cancel the common factor $c$ in the numerator and denominator:
$\frac{4c}{7c + 2}$
The simplified expression is:
$\frac{4c}{7c + 2}$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms