Question

Solve the following equation:  `"a"/("x" - "a") + "b"/("x" - "b") = (2"c")/("x" - "c")`

Answer 1

`"a"/("x" - "a") + "b"/("x" - "b") = (2"c")/("x" - "c")`

`("a"("x" - "b") + "b"("x" - "a"))/(("x" - "a")("x" - "b")) = (2"c")/("x" - "c")`

`("ax - ab + bx - ab")/("x"^2 - "ax" - "bx" + "ab") = (2"c")/("x" - "c")`

`(("a + b")"x" - 2 "ab")/("x"^2 - ("a + b")"x" + "ab") = (2"c")/("x" - "c")`

{(a+ b) x- 2ab} (x- c) = 2c {x² - (a + b) x + ab} 

(a+ b )x² - 2abx - c (a+ b )x + 2abc = 2cx² - 2c( a+ b )x + 2abc 

(a+ b )x² - [2ab + c( a+ b )]x + 2abc = 2cx² - 2c( a+ b )x + 2abc 

(a+ b-2c)x² = (2ab + ac+ bc- 2ca - 2bc)x 

(a+ b-2c )x² = (2ab - ac - bc) x 

x = 0 , x = `(2"ab" - "ac" - "bc")/("a" + "b" - 2"c")`