Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Dec 16, 2023

Simplify the expression $\frac{11(x-3) \cdot 7 \cdot 7}{5 \cdot 7 \cdot 5 \cdot 11(x-3)}$ by dividing out common factors.

STEP 1

Assumptions
1. We are given a fraction that needs to be simplified.
2. We will simplify by canceling out common factors in the numerator and the denominator.

STEP 2

Identify the common factors in the numerator and the denominator.
The common factors are $11$ , $(x-3)$ , and $7$ .

STEP 3

Cancel out the common factor of $11$ from the numerator and the denominator.
$\frac{11(x-3) \cdot 7 \cdot 7}{5 \cdot 7 \cdot 5 \cdot 11(x-3)} = \frac{\cancel{11}(x-3) \cdot 7 \cdot 7}{5 \cdot 7 \cdot 5 \cdot \cancel{11}(x-3)}$

STEP 4

Cancel out the common factor of $(x-3)$ from the numerator and the denominator.
$\frac{\cancel{11}\cancel{(x-3)} \cdot 7 \cdot 7}{5 \cdot 7 \cdot 5 \cdot \cancel{11}\cancel{(x-3)}} = \frac{7 \cdot 7}{5 \cdot 7 \cdot 5}$

STEP 5

Cancel out the common factor of $7$ from the numerator and the denominator.
$\frac{7 \cdot 7}{5 \cdot \cancel{7} \cdot 5} = \frac{7}{5 \cdot 5}$

STEP 6

Now that we have canceled out all the common factors, we can write the simplified fraction.
$\frac{7}{5 \cdot 5} = \frac{7}{25}$
The product in lowest terms is $\frac{7}{25}$ .

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