Exercises with Solutions
Exercises with Solutions
Exercises with Solutions
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Chapter 7<br />
Rational Functions<br />
7.8 <strong>Solutions</strong><br />
1. Start <strong>with</strong> the equation<br />
1<br />
x + 1<br />
x + 2 = −16 63<br />
Multiply both sides by the LCD 63x(x + 2):<br />
Simplify to obtain<br />
63(x + 2) + 63x = −16x(x + 2)<br />
126x + 126 = −16x 2 − 32x<br />
This quadratic equation has one integer solution x = −9, and the second number is<br />
−9 + 2 = −7.<br />
3. Start <strong>with</strong> the equation<br />
1<br />
x + 1<br />
x + 1 = −19 90<br />
Multiply both sides by the LCD 90x(x + 1):<br />
Simplify to obtain<br />
90(x + 1) + 90x = −19x(x + 1)<br />
180x + 90 = −19x 2 − 19x<br />
This quadratic equation has one integer solution x = −10, and the second number is<br />
−10 + 1 = −9.<br />
5. Start <strong>with</strong> the equation<br />
1<br />
x + 1<br />
x + 2 = 5 12<br />
Multiply both sides by the LCD 12x(x + 2):<br />
Simplify to obtain<br />
12(x + 2) + 12x = 5x(x + 2)<br />
24x + 24 = 5x 2 + 10x<br />
This quadratic equation has one integer solution x = 4, and the second number is<br />
4 + 2 = 6.<br />
Version: Fall 2007
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