Question

x-6/6+x-3/10=x-4/4
can you please tell me the answer

Answer 1

Given

$\tt \to \: \dfrac{x - 6}{6} + \dfrac{x - 3}{10} = \dfrac{x - 4}{4}$

Now Take LCM on LHS

$\tt \to \: \dfrac{5(x - 6)}{6 \times 5} + \dfrac{3(x - 3)}{10 \times 3} = \dfrac{x - 4}{4}$

$\tt \to \: \dfrac{5(x - 6) + 3(x - 3)}{30} = \dfrac{x - 4}{4}$

$\tt \to \: \dfrac{5x - 30 + 3x - 9}{30} = \dfrac{x - 4}{4}$

$\tt \to \: \dfrac{8x - 39 }{30} = \dfrac{x - 4}{4}$

Using cross Multiplication method

$\tt \to4(8x - 39) = 30(x - 4)$

$\tt \to \: 32x - 156 = 30x - 120$

$\tt \to \: 32x - 30x = 156 - 120$

$\tt \to \: 2x = 36$

$\tt \to \: x = \dfrac{36}{2}$

$\tt \to \: x = 18$

Answer

$\tt \to \: x = 18$

Now Check our result

$\tt \to \: \dfrac{x - 6}{6} + \dfrac{x - 3}{10} = \dfrac{x - 4}{4}$

Put the value of x = 18

$\tt \to \: \dfrac{18 - 6}{6} + \dfrac{18 - 3}{10} = \dfrac{18 - 4}{4}$

$\tt \to \: \dfrac{12}{6} + \dfrac{15}{10} = \dfrac{14}{4}$

$\tt \to \: 2 + \dfrac{3}{2} = \dfrac{7}{2}$

$\tt \to \: \dfrac{4 + 3}{2} = \dfrac{7}{3}$

$\tt \to \: \dfrac{7}{3} = \dfrac{7}{3}$

LHS = RHS

Answer 2

${\huge{\green{Explain:-}}}$

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

LCM of x - 5, x - 7, 3  = 3(x - 5)(x-7).

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

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

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

6x^2 - 66x + 174 - 10x^2 + 120x - 350 = 0

-4x^2 + 54x - 176 = 0 

= -(2x^2 - 27x + 88) = 0

2x^2 - 27x + 88 = 0

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

2x(x - 8) - 11(x - 88) = 0

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

x = 11/2, x = 8.

Hope this helps!