Question

solve the equation (x-a)(x-b)/x-a-b=(x-c)(x-d)/x-c-d​

Answer 1

Answer:

x = (ab(c + d) - cd(a +b))/(ab -cd)

Step-by-step explanation:

solve the equation (x-a)(x-b)/x-a-b=(x-c)(x-d)/x-c-d​

(x-a)(x-b)/(x-a-b) = (x-c)(x-d)/(x-c-d)

=> (x-a)(x-b)(x-c-d) = (x-c)(x-d)(x-a-b)

=> (x-a)(x-b)x - (x-a)(x-b)(c+d) = (x-c)(x-d)x - (x-c)(x-d)(a+b)

=> x(​(x-a)(x-b) -  (x-c)(x-d)) = (x-a)(x-b)(c+d) - (x-c)(x-d)(a+b)

=> x(x² -ax -bx + ab - x² + cx + dx -cd) = (x² -ax -bx + ab)(c +d) - (x² -cx -dx + cd)(a+b)

=> x(-ax - bx + cx  + dx + ab - cd) = cx² -acx -bcx + abc +dx² -adx -bdx + abd -(ax² -acx -adx + acd + bx² -bcx -bdx + bcd)

=> -ax² -bx² + cx² + dx² + abx - cdx = cx² -acx -bcx + abc +dx² -adx -bdx + abd -ax² + acx +adx -acd -bx² + bcx + bdx -bcd)

Cancelling  -ax² -bx² + cx² + dx² from both sides

=> abx - cdx = abc  + abd - acd - bcd

=> x(ab - cd) = ab(c + d) - cd(a +b)

=> x = (ab(c + d) - cd(a +b))/(ab -cd)