Question

Solve for x: 3 over 3 x plus 1 over quantity x plus 4 equals 10 over 7x .

Answer 1

  3              1                   10
------ + --------------- =  ----------
 3x          x +4                 7x

      1            1                 10
    ------ + ------------ =  ----------
      x          x +4               7x


       x + 4 + x           10               
   ------------------ =  ----------
       x(x +4)             7x

       2x + 4                10               
 ------------------ =  ----------
       x(x +4)                7x

    7x(2x + 4) = 10x(x+4)
  
  14x^2 + 28x = 10x^2 + 40x

  4x^2  - 12x = 0
  4x(x - 3) = 0
  4x = 0
    x = 0
 x - 3 = 0
      x = 3

answer x = 0 and x = 3

Answer 2

Answer:

The value of x is:

                                3

Step-by-step explanation:

We are asked to solve:

   $\dfrac{3}{x}+\dfrac{1}{x+4}=\dfrac{10}{7x}$

on taking least common multiple in the left hand side of the equation we get:

    $\dfrac{3(x+4)+3x}{3x(x+4)}=\dfrac{10}{7x}\\\\\\\dfrac{3x+12+3x}{3x(x+4)}=\dfrac{10}{7x}\\\\\\\dfrac{6x+12}{3x(x+4)}=\dfrac{10}{7x}\\\\\\7x(6x+12)=10(3x(x+4))\\\\\\x(42x+84)=x(30x+120)\\\\\\x(42x+84-30x-120)=0\\\\\\x=0\ or\ 12x-36=0\\\\\\x=0\ or\\\\\\12x=36\\\\\\i.e.\\\\\\x=0\ or\ x=3$

But x≠0

because if x=0 then,

         $\dfrac{1}{3x}$ will not be defined.

 Hence, the value of x is:

                     3