Question

Solve for x. x -4 / x-5+x-6/x-7=10/3

Answer 1

Given: The equation: x -4 / x-5+x-6/x-7=10/3

To find: Solve for x?

Solution:

• Now we have given:

                 x -4 / x-5 + x-6/x-7=10/3

• Cross multiplying, we get:

                 (x-4)(x-7) + (x-6)(x-5) = 10(x-5)(x-7)/3

                 3(x² - 7x - 4x + 28 + x² - 5x - 6x + 30) = 10(x² - 7x - 5x + 35)

                 6x² - 66x + 174 = 10x² - 120x + 350

                 10x² - 120x + 350 - 6x² + 66x - 174 = 0

                 4x² - 54x + 176 = 0

                 2x² - 27x + 88 = 0

                 x = 27 ± √((-27)²-4(2)(88)) / 2(2)

                 x = 27 ± √(729-704) / 4

                 x = 27 ± √25 / 4

                 x = 27 ± 5 / 4

                 x = 32/4 , 22/4

                 x = 8, 11/2

Answer:

              So the value of x is 8, 11/2.