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Answer:
[tex]\displaystyle x=\frac{a+b}{c}[/tex]
Step-by-step explanation:
Equations
Solve the equation:
[tex]\displaystyle \frac{b-cx}{a}+\frac{a-cx}{b}+2=0[/tex]
Subtracting 2:
[tex]\displaystyle \frac{b-cx}{a}+\frac{a-cx}{b}=-2[/tex]
Multiply by ab to eliminate denominators:
[tex]\displaystyle ab\frac{b-cx}{a}+ab\frac{a-cx}{b}=-2ab[/tex]
Simplifying:
[tex]b(b-cx)+a(a-cx)=-2ab[/tex]
Operating:
[tex]b^2-bcx+a^2-acx=-2ab[/tex]
Subtracting [tex]b^2+a^2[/tex]
[tex]-bcx-acx=-2ab-b^2-a^2[/tex]
Multiplying by -1:
[tex]bcx+acx=2ab+b^2+a^2[/tex]
Factoring:
[tex]c(b+a)x=2ab-b^2+a^2[/tex]
The right side of the equation is the square of a+b:
[tex]c(b+a)x=(a+b)^2[/tex]
Simplifying (for a ≠ -b):
[tex]cx=(a+b)[/tex]
Dividing by c:
[tex]\boxed{\displaystyle x=\frac{a+b}{c}}[/tex]