To divide these fractions, you need to understand that dividing by a fraction is the same as multiplying by its reciprocal. Here's the given expression broken down:
\[
\frac{7/x + 2}{9/3x + 6}
\]
First, let's rewrite this expression in a clearer format:
\[
\frac{\frac{7}{x} + 2}{\frac{9}{3x} + 6}
\]
Now, simplify the expressions in the numerator and the denominator:
Numerator:
\[
\frac{7}{x} + 2
\]
Denominator:
\[
\frac{9}{3x} + 6
\]
Let's simplify the denominator step by step:
\[
\frac{9}{3x} = \frac{9}{3} \cdot \frac{1}{x} = 3 \cdot \frac{1}{x} = \frac{3}{x}
\]
Therefore, the denominator becomes:
\[
\frac{3}{x} + 6
\]
Now the entire expression is:
\[
\frac{\frac{7}{x} + 2}{\frac{3}{x} + 6}
\]
To divide these complex fractions, multiply the numerator by the reciprocal of the denominator:
\[
\left(\frac{7/x + 2}{1}\right) \times \left(\frac{1}{\frac{3/x + 6}{1}}\right)
\]
This simplifies to:
\[
\left(\frac{7 + 2x}{x}\right) \times \left(\frac{x}{3 + 6x}\right)
\]
Notice that you can cancel out the \(x\) in the numerator and denominator:
\[
= \frac{7 + 2x}{3 + 6x}
\]
So, the simplified expression is:
\[
\frac{7 + 2x}{3 + 6x}
\]
This is the most simplified form of the given expression.
divide these fractions
7/x+2/9/3x+6
1 answer