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(x-1)/(5-x)=2/9

(x-1)/(5-x)=2/9 equation

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Numerical solution:

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The solution

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x - 1      
----- = 2/9
5 - x
x−15−x=29\frac{x - 1}{5 - x} = \frac{2}{9}
Simplify
Detail solution
Given the equation:
x−15−x=29\frac{x - 1}{5 - x} = \frac{2}{9}
Multiply the equation sides by the denominator 5 - x
we get:
(1−x)(5−x)x−5=109−2x9\frac{\left(1 - x\right) \left(5 - x\right)}{x - 5} = \frac{10}{9} - \frac{2 x}{9}
Expand brackets in the left part
1+x5+x-5+x = 10/9 - 2*x/9

Looking for similar summands in the left part:
(1 - x)*(5 - x)/(-5 + x) = 10/9 - 2*x/9

Move free summands (without x)
from left part to right part, we given:
(1−x)(5−x)x−5+5=559−2x9\frac{\left(1 - x\right) \left(5 - x\right)}{x - 5} + 5 = \frac{55}{9} - \frac{2 x}{9}
Move the summands with the unknown x
from the right part to the left part:
2x9+(1−x)(5−x)x−5+5=559\frac{2 x}{9} + \frac{\left(1 - x\right) \left(5 - x\right)}{x - 5} + 5 = \frac{55}{9}
Divide both parts of the equation by (5 + 2*x/9 + (1 - x)*(5 - x)/(-5 + x))/x
x = 55/9 / ((5 + 2*x/9 + (1 - x)*(5 - x)/(-5 + x))/x)

We get the answer: x = 19/11
The graph
-10.0-7.5-5.0-2.50.02.55.07.510.012.515.017.5-1000010000
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
     19
x1 = --
     11
x1=1911x_{1} = \frac{19}{11} 
x1 = 19/11
Sum and product of roots [src] 
sum
19
--
11
1911\frac{19}{11} 
=
19
--
11
1911\frac{19}{11} 
product
19
--
11
1911\frac{19}{11} 
=
19
--
11
1911\frac{19}{11} 
19/11
Numerical answer [src] 
x1 = 1.72727272727273
x1 = 1.72727272727273
The graph
(x-1)/(5-x)=2/9 equation
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