Q32. Simplify the expression聽5x2+10x... [FREE SOLUTION]

Chapter 9: Q32. (page 476)

Simplify the expression $\frac{5 x^{2} + 10 x 鈭� 75}{4 x^{2} 鈭� 24 x 鈭� 28} 鈰� \frac{2 x^{2} 鈭� 10 x 鈭� 28}{x^{2} + 7 x + 10}$

Short Answer

Expert verified

The simplified value of expression is $\frac{5 (x 鈭� 3)}{2 (x + 1)}$

Step by step solution

Step 1. Write down the given expression.

The given expression is $\frac{5 x^{2} + 10 x 鈭� 75}{4 x^{2} 鈭� 24 x 鈭� 28} 鈰� \frac{2 x^{2} 鈭� 10 x 鈭� 28}{x^{2} + 7 x + 10}$

Step 2. Simplify the expression.

The given expression $\frac{5 x^{2} + 10 x 鈭� 75}{4 x^{2} 鈭� 24 x 鈭� 28} 鈰� \frac{2 x^{2} 鈭� 10 x 鈭� 28}{x^{2} + 7 x + 10}$ is simplified as:

$\begin{matrix} \frac{5 x^{2} + 10 x 鈭� 75}{4 x^{2} 鈭� 24 x 鈭� 28} 鈰� \frac{2 x^{2} 鈭� 10 x 鈭� 28}{x^{2} + 7 x + 10} = \frac{5 (x^{2} + 2 x 鈭� 15)}{4 (x^{2} 鈭� 6 x 鈭� 7)} 鈰� \frac{2 (x^{2} 鈭� 5 x 鈭� 14)}{x^{2} + 7 x + 10} \\ = \frac{5 (x + 5) (x 鈭� 3)}{4 (x 鈭� 7) (x + 1)} 鈰� \frac{2 (x 鈭� 7) (x + 2)}{(x + 5) (x + 2)} \\ = \frac{5}{2} 鈰� \frac{(x 鈭� 7) (x + 2) (x + 5) (x 鈭� 3)}{(x + 5) (x + 2) (x 鈭� 7) (x + 1)} \\ = \frac{5 (x 鈭� 3)}{2 (x + 1)} \end{matrix}$

Step 3. Conclusion.

The simplified value of expression is $\frac{5 (x 鈭� 3)}{2 (x + 1)}$

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Simplify the expression $\frac{5 x^{2} + 10 x 鈭� 75}{4 x^{2} 鈭� 24 x 鈭� 28} 鈰� \frac{2 x^{2} 鈭� 10 x 鈭� 28}{x^{2} + 7 x + 10}$

Short Answer

Step by step solution

Step 1. Write down the given expression.

Step 2. Simplify the expression.

Step 3. Conclusion.

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Simplify the expression5x2+10x鈭�754x2鈭�24x鈭�28鈰�2x2鈭�10x鈭�28x2+7x+10

Short Answer

Step by step solution

Step 1. Write down the given expression.

Step 2. Simplify the expression.

Step 3. Conclusion.

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Logic and Functions

Geometry

Discrete Mathematics

Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Simplify the expression $\frac{5 x^{2} + 10 x 鈭� 75}{4 x^{2} 鈭� 24 x 鈭� 28} 鈰� \frac{2 x^{2} 鈭� 10 x 鈭� 28}{x^{2} + 7 x + 10}$