Solve for x :
(x-a / x-b) + (x-b / x-a) = (a/b) + (b/a)
Answers
Answered by
370
( x -a)/(x -b) + ( x -b)/( x - a) =a/b + b/a
{(x -a)² + (x -b)² }/(x -a)(x -b) ={ a² +b²}/ab
ab{ (x² -2a +a² + x² -2b +b²) = (a² + b²)(x² -ax -bx + ab)
ab{ 2x² -2(a + b)x +(a² + b²)} =(a² +b²)x² -(a² +b²)(a +b)x +(a² + b²)ab
(2ab -a² -b²)x² -(a +b)(2ab -a² -b²)x =0
(a² + b² -2ab)x² -(a +b)(a² +b² -2ab)x =0
(a -b)²x² -(a+b)(a-b)² x =0
x² -(a + b)x =0
x{ x -(a + b)} =0
x =0, (a + b)
{(x -a)² + (x -b)² }/(x -a)(x -b) ={ a² +b²}/ab
ab{ (x² -2a +a² + x² -2b +b²) = (a² + b²)(x² -ax -bx + ab)
ab{ 2x² -2(a + b)x +(a² + b²)} =(a² +b²)x² -(a² +b²)(a +b)x +(a² + b²)ab
(2ab -a² -b²)x² -(a +b)(2ab -a² -b²)x =0
(a² + b² -2ab)x² -(a +b)(a² +b² -2ab)x =0
(a -b)²x² -(a+b)(a-b)² x =0
x² -(a + b)x =0
x{ x -(a + b)} =0
x =0, (a + b)
abhi178:
now see the answer
Thanks
It's correct
yh!
yes its correct
i hpe you understand concept here
Answered by
47
Answer:
( x -a)/(x -b) + ( x -b)/( x - a) =a/b + b/a
{(x -a)² + (x -b)² }/(x -a)(x -b) ={ a² +b²}/ab
ab{ (x² -2a +a² + x² -2b +b²) = (a² + b²)(x² -ax -bx + ab)
ab{ 2x² -2(a + b)x +(a² + b²)} =(a² +b²)x² -(a² +b²)(a +b)x +(a² + b²)ab
(2ab -a² -b²)x² -(a +b)(2ab -a² -b²)x =0
(a² + b² -2ab)x² -(a +b)(a² +b² -2ab)x =0
(a -b)²x² -(a+b)(a-b)² x =0
x² -(a + b)x =0
x{ x -(a + b)} =0
x =0, (a + b)
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