Question

find the solution of equation x-4/x-5+x-6/x-7=10/23 ,x is not equal to 5,7​

Answer 1

Therefore, we can say that the solutions are $x=11/2$ or $x=8$

Given:

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

x is not equal to 5,7

To find:

The solution to the equation x-4/x-5 + x-6/x-7 = 10/3

Solution:

Here an equation is provided with an unknown term. This term cannot be 5 or 7 since any number cannot be divisible by 5 or 7.

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

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

$x^2-7x-4x+28+x^2-5x-6x+30/x^2-7x-5x+35$

$2x^2-22x+58/x^2-12x-5x+35/x^2-12x+35 = 10/3$

$3x^2-33x+87 = 5x^2-60x+175$

$2x^2-27x+145=0$

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

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

$x=11/2$ or $x=8$

Try substituting both values and find out if LHS is equal to RHS in one of the equations solved above.

Therefore, we can say that the solutions are $x=11/2$ or $x=8$

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