Solve by factorization: `a/(x-a)+b/(x-b)=(2c)/(x-c)`

Solve by factorization: x^2+2a b=(2a+b)x

Solve by factorization: a^2x^2-3a b x+2b^2=0

Solve by factorization: 9x^2-6b^2x-(a^4-b^4)=0

Solve by factorization: a b x^2+(b^2-a c)x-b c=0

Solve the following quadratic equations by factorization: (x-a)/(x-b)+(x-b)/(x-a)=a/b+b/a

Solve by factorization: (a+b)^2x^2-4a b x-(a-b)^2=0

Solve by factorization: 4x^2+4b x-(a^2-b^2)=0

Solve by factorization: a x^2+(4a^2-3b)x-12 a b=0

Solve for x in R : |((x+a)(x-a),(x+b)(x-b),(x+c)(x-c)),((x-a)^3,(x-b)^3,(x-c)^3),((x+a)^3,(x+b)^3,(x+c)^3)| =0, a,b and c being distinct real numbers.

A root of the equation (a+c)/(x+a)+(b+c)/(x+b)=(2(a+b+c))/(x+a+b) is