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solve the following equation for x (linear equation):
[tex]\frac{b-cx}{a} + \frac{a-cx}{b} + 2 = 0[/tex]


Sagot :

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]