Chapter 7 linear equaTionS 217

4.^6741 xx+− =^3824 xx+− This is in the form “Fraction = Fraction,” so cross-multiply.

() 67 () 24 () 41 () 38

12 2224 14 28 12

xx xx

xxxx

+−=−+

−+−=+ 332 38

12 10 28 12 29 812

10

222

xx

xx xx x

−−

−−=+−

−

,scancel

xxx

xx

x

x

−= −

++

−= −

++

−=

28 29 8

10 10

28 39 8

88

20 39

− (^20) =
39
x
5.
9
1
3
31
x
3 xx
4
−
=+
−^ The LCD is 3x − 1.
() ()
()
319
31
314 3
31
931
x x
x
x
x
xx
−
−




=−+
−




=−(()()
431 3
31
91243
9121
99
+−
−




=−+
=−
−−
x
x
xx
xx
x xx
x
x
x
031
11
13
1
3
=−
++

=
If we let x=^13 , then both denominators would be 0, so x=^13 is not a
solution to the original equation. The original equation has no solution.