Solve for h: h/3-4 ((2 h)/3-3) = (2 h)/3-6 Put each term in (2 h)/3-3 over the common denominator 3: (2 h)/3-3 = (2 h)/3-(9)/3: h/3-4(2 h)/3-(9)/3 = (2 h)/3-6 (2 h)/3-(9)/3 = (2 h-9)/3: h/3-4(2 h-9)/3 = (2 h)/3-6 h/3-(4 (2 h-9))/3 = (h-4 (2 h-9))/3: (h-4 (2 h-9))/3 = (2 h)/3-6 -4 (2 h-9) = 36-8 h: (h+36-8 h)/3 = (2 h)/3-6 h-8 h = -7 h: (-7 h+36)/3 = (2 h)/3-6 Put each term in (2 h)/3-6 over the common denominator 3: (2 h)/3-6 = (2 h)/3-(18)/3: (36-7 h)/3 = (2 h)/3-(18)/3 (2 h)/3-(18)/3 = (2 h-18)/3: (36-7 h)/3 = (2 h-18)/3 Multiply both sides by 3: 36-7 h = 2 h-18 Subtract 2 h from both sides: 36+(-7 h-2 h) = (2 h-2 h)-18 -7 h-2 h = -9 h: -9 h+36 = (2 h-2 h)-18 2 h-2 h = 0: 36-9 h = -18 Subtract 36 from both sides: (36-36)-9 h = -18-36 36-36 = 0: -9 h = -18-36 -18-36 = -54: -9 h = -54 Divide both sides of -9 h = -54 by -9: (-9 h)/(-9) = (-54)/(-9) (-9)/(-9) = 1: h = (-54)/(-9) The gcd of -54 and -9 is -9, so (-54)/(-9) = (-9×6)/(-9×1) = (-9)/(-9)×6 = 6: Answer: | | h = 6
+2592 1/3h-4(2/3h-3)=2/3h-6
1/3h-8/3h+12=2/3h-6
-7/3h+12=2/3h-6
12=9/3h-6
18=3h
h=6
