Chapter 10 QuadratiC EQuations 375

Solve the equation.

3

4

624

x^228

x

− xx

= −+

−−

We begin with cross-multiplication.

32 ()xx^2 −−=−−+ 84 ()xx() 624 Thisisthecross-multipplicationstep.

36 xx^22 −− 24 =− +− 64 xx 896 UsetheFOIILmethod ontheright.

+− 64 xx^2289 ++ 66 xx−+ 48 96 Reewritewith0ononeside.

95 xx^2 −+ 4720 =

1

9

95472 1

9

()xx^2 −+= () 0 Eachtermisdivisibleby9.

xx

xx

(^2680)
420
−+=
()−−()=
xx
xx
−= −=

40 20
42
We cannot let x be 4 because x = 4 leads to a zero in the denominator
of^3
x –  4
.
The only solution, then, is x = 2.
PRACTICE
Solve the equation. (Because all of these problems factor, factoring is used
in the solutions. If factoring takes too long on some of these, you may use
the quadratic formula.)

1.^3
4

3

2

x

x

x

−

=−

2. x
   xx

−

+

=

−

1

23

6

2

3. x
   x

x

x

x

x

+

−

+ +

−

= +

+

2

3

21

9

12 3

(^23)
PRACTICE
Solve the equation. (Because all of these problems factor, factoring is used
in the solutions. If factoring takes too long on some of these, you may use
the quadratic formula.)
PRACTICE
Solve the equation. (Because all of these problems factor, factoring is used