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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

You have entered [src]
x - 1      
----- = 2/9
5 - x      
x15x=29\frac{x - 1}{5 - x} = \frac{2}{9}
Detail solution
Given the equation:
x15x=29\frac{x - 1}{5 - x} = \frac{2}{9}
Multiply the equation sides by the denominator 5 - x
we get:
(1x)(5x)x5=1092x9\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:
(1x)(5x)x5+5=5592x9\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+(1x)(5x)x5+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
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