Question

Solve for x: (x-4)/(x-5)+(x-6)/(x-7)=10/3;x≠5,7

Answer 1

\(\frac{x - 4}{x - 5} + \frac{x - 6}{x - 7} = \frac{10}3\)

⇒ \(\frac{(x - 4)(x - 7)+(x - 6)(x - 5)}{(x - 5)(x - 7)} = \frac{10}3\)

⇒ \(\frac{x^2 - 7x - 4x + 28 + x^2 - 5x - 6x + 30}{x^2 - 7x - 5x + 35} = \frac{10}3\)

⇒ \(\frac{2x^2 - 22x + 58}{x^2 -12x + 35} = \frac{10}3\)

⇒ \(\frac{x^2 - 11x + 29}{x^2 -12x + 35} = \frac{5}3\)

⇒ 3x² − 33x + 87 = 5x² − 60x + 175

⇒ 2x² − 27x + 88 = 0

⇒ 2x(x − 8) − 11(x − 8) = 0

⇒ (2x − 11)(x − 8) = 0

⇒ 2x − 11 = 0 or x − 8 = 0

⇒ x = \(\frac{11}2\) or x = 8

Answer 2

Answer is....