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.