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solve the rational equation x over 3 equals x squared over quantity x plus 5 and check for extraneous solutions.

a. x = 0; x equals negative five halves is an extraneous solution
b. x equals five halves; x = 0 is an extraneous solution
c. x = 0 and x equals five halves
d. x = 0 and x equals negative five halves

x/3=x^2/x+5

First cross multiply to get rid of the fractions.

x^2+5x=3x^2

Simplify by combining like terms.

-2x^2+5x=0

Factor out x.

x(-2x+5)=0

One of the factors must equal zero for the equation to stand.

x=0,2.5

Check for extraneous solutions by plugging in the values for x. They both work.

C

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above