Question

Solve for x x minus 4 upon x minus 5 + x minus 6 upon x minus 7 equal to 10 upon 3 but x does not equal to 5 or 7

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

Value of x is 8 and 5.5

Step-by-step explanation:

Given: $\frac{x-4}{x-5}+\frac{x-6}{x-7}=\frac{10}{3}$

To find: Value of x

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

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

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

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

$3(2x^2-22x+58)=10(x^2-12x+35)$

$6x^2-66x+174=10x^-120x+350$

$4x^2-54x+176=0$

$2x^2-27x+88=0$

$2x^2-16x-11x+88=0$

$2x(x-8)-11(x-8)=0$

$(x-8)(2x-11)=0$

So,

x - 8 = 0  ⇒ x = 8

2x - 11 = 0 ⇒ x = 5.5

Therefore, Value of x is 8 and 5.5