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13/(x-5)=5/(x-13)

13/(x-5)=5/(x-13) equation

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Numerical solution:

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The solution

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  13      5   
----- = ------
x - 5   x - 13
13x−5=5x−13\frac{13}{x - 5} = \frac{5}{x - 13}
Simplify
Detail solution
Given the equation:
13x−5=5x−13\frac{13}{x - 5} = \frac{5}{x - 13}
Use proportions rule:
From a1/b1 = a2/b2 should a1*b2 = a2*b1,
In this case
a1 = 13

b1 = -5 + x

a2 = 5

b2 = -13 + x

so we get the equation
13(x−13)=5(x−5)13 \left(x - 13\right) = 5 \left(x - 5\right)
13x−169=5x−2513 x - 169 = 5 x - 25
Move free summands (without x)
from left part to right part, we given:
13x=5x+14413 x = 5 x + 144
Move the summands with the unknown x
from the right part to the left part:
8x=1448 x = 144
Divide both parts of the equation by 8
x = 144 / (8)

We get the answer: x = 18
The graph
828101214161820222426-5000050000
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 18
x1=18x_{1} = 18 
x1 = 18
Sum and product of roots [src] 
sum
18
1818 
=
18
1818 
product
18
1818 
=
18
1818 
18
Numerical answer [src] 
x1 = 18.0
x1 = 18.0
The graph
13/(x-5)=5/(x-13) equation
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