## Algebra 1

Published by Prentice Hall

# Chapter 11 - Rational Expressions and Functions - 11-1 Simplifying Rational Expressions - Practice and Problem-Solving Exercises - Page 656: 40

#### Answer

$\frac{x}{16+2x}$

#### Work Step by Step

Find the area of the triangle, using A=$\frac{1}{2}$bh. The base is x and the height is x. $$\frac{(x)(x)}{2} = \frac{x^{2}}{2}$$ Find the area of the rectangle, using A=lw. The length is 8+x and the width is x $$x\times(8+x)=8x+x^{2}$$ Find the ratio by dividing the area of the triangle by the area of the rectangle. Dividing is equivalent to multiplying by the reciprocal of a number. $$(\frac{x^{2}}{2})\div(8x+x^{2}) = \frac{x^2}{(2)\times(8x+x^2)} = \frac{x^2}{16x+2x^2} = \frac{x}{16+2x}$$ The length of the rectangle is given by $L = 8+x$ The area of the triangle is given by $A=\frac{1}{2}bh$ or $A=\frac{bh}{2}$

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