Questions: (5x-35)/27 ÷ (8x-63)/18 = □

Transcript text: \[ \frac{5 x-35}{27} \div \frac{8 x-63}{18}=\square \]

Solution

Solution Steps

To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. Simplify the resulting expression if possible.

Step 1: Define the Fractions

We start with the two fractions: \[ \frac{5x - 35}{27} \quad \text{and} \quad \frac{8x - 63}{18} \]

Step 2: Multiply by the Reciprocal

To divide the first fraction by the second, we multiply by the reciprocal of the second fraction: \[ \frac{5x - 35}{27} \div \frac{8x - 63}{18} = \frac{5x - 35}{27} \cdot \frac{18}{8x - 63} \]

Step 3: Simplify the Expression

This results in: \[ \frac{18(5x - 35)}{27(8x - 63)} \] We can simplify this further: \[ = \frac{2(5x - 35)}{3(8x - 63)} \] This can be expressed as: \[ = \frac{10(x - 7)}{3(8x - 63)} \]

Final Answer

Thus, the simplified result of the division is: \[ \boxed{\frac{10(x - 7)}{3(8x - 63)}} \]

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