Chapter 12: Q41. (page 637)

Simplify each expression.
$\frac{\frac{x^{2}}{x^{2} - 25 y^{2}}}{\frac{x}{5 y - x}}$

Short Answer

Expert verified

The simplified value of expression is $\frac{\frac{x^{2}}{x^{2} - 25 y^{2}}}{\frac{x}{5 y - x}} = - \frac{x}{x + 5 y}$ .

Step by step solution

Step 1. Given Information.

The given expression to simplify is $\frac{\frac{x^{2}}{x^{2} - 25 y^{2}}}{\frac{x}{5 y - x}}$ .

Step 2. Calculation.

Simplifying the expression:

$\begin{array}{l} \frac{\frac{x^{2}}{x^{2} - 25 y^{2}}}{\frac{x}{5 y - x}} = \frac{x^{2}}{x^{2} - 25 y^{2}} \cdot \frac{5 y - x}{x} (Writingthedenominatorasaproductofreciprocal) \\ \frac{\frac{x^{2}}{x^{2} - 25 y^{2}}}{\frac{x}{5 y - x}} = \frac{x^{2} (5 y - x)}{(x^{2} - 25 y^{2}) x} \\ \frac{\frac{x^{2}}{x^{2} - 25 y^{2}}}{\frac{x}{5 y - x}} = \frac{x \cdot x \cdot - (x - 5 y)}{(x - 5 y) (x + 5 y) x} (Factoringthenumeratoranddenominator) \\ \frac{\frac{x^{2}}{x^{2} - 25 y^{2}}}{\frac{x}{5 y - x}} = - \frac{x}{x + 5 y} (Cancellingoutthecommontermsfromnumeratoranddenominator) \end{array}$

Step 3. Conclusion.

The simplified value of expression is $\frac{\frac{x^{2}}{x^{2} - 25 y^{2}}}{\frac{x}{5 y - x}} = - \frac{x}{x + 5 y}$ .

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Simplify each expression.
$\frac{\frac{x^{2}}{x^{2} - 25 y^{2}}}{\frac{x}{5 y - x}}$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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Simplify each expression.x2x2−25y2x5y−x

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

Simplify each expression.
$\frac{\frac{x^{2}}{x^{2} - 25 y^{2}}}{\frac{x}{5 y - x}}$