SOLUTION: Given that {{{3 / (x + 1) - 5 / (y - 2) = 1 / (z - 3)}}}, find a simplified expression for x.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Given that {{{3 / (x + 1) - 5 / (y - 2) = 1 / (z - 3)}}}, find a simplified expression for x.      Log On


   

Question 1205481: Given that 3+%2F+%28x+%2B+1%29+-+5+%2F+%28y+-+2%29+=+1+%2F+%28z+-+3%29, find a simplified expression for x.
Found 2 solutions by MathLover1, josgarithmetic:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

3+%2F+%28x+%2B+1%29+-+5+%2F+%28y+-+2%29+=+1+%2F+%28z+-+3%29

3+%2F+%28x+%2B+1%29+=+5+%2F+%28y+-+2%29+%2B1+%2F+%28z+-+3%29

3+%2F+%28x+%2B+1%29+=+%285%28z+-+3%29++%2B1%28y+-+2%29%29+%2F%28%28y+-+2%29+%28z+-+3%29%29

3+%2F+%28x+%2B+1%29+=+%28y+%2B+5z+-+17%29%2F%28%28y+-+2%29%28z+-+3%29%29....cross multiply

3%28%28y+-+2%29%28z+-+3%29%29++=+%28x+%2B+1%29%28y+%2B+5z+-+17%29

3%28%28y+-+2%29%28z+-+3%29%29%2F%28y+%2B+5z+-+17%29++=+%28x+%2B+1%29

x=3%28%28y+-+2%29%28z+-+3%29%29%2F%28y+%2B+5z+-+17%29++-+1



x=%283%28%28y+-+2%29%28z+-+3%29%29+-+%28y+%2B+5z+-+17%29%29%2F%28y+%2B+5z+-+17%29

x=%283yz+-+10y+-+11z+%2B+35%29%2F%28y+%2B+5z+-+17%29



Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
A few algebra steps in which watching every piece of every step needs delicate detail.
Starting may be with 3%2F%28x%2B1%29=1%2F%28z-3%29%2B5%2F%28y-2%29, and multiply both sides by the common denominator,
and then those careful steps,
..
.
.
THIS still needs further simplification:
x=%283%28z-3%29%28y-2%29%2B17-y-5z%29%2F%28y%2B5z-17%29




(note: not yet checked for mistakes)