Respuesta :
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
------ + --------------- = ----------
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:
The value of x is:
3
Step-by-step explanation:
We are asked to solve:
[tex]\dfrac{3}{x}+\dfrac{1}{x+4}=\dfrac{10}{7x}[/tex]
on taking least common multiple in the left hand side of the equation we get:
[tex]\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[/tex]
But x≠0
because if x=0 then,
[tex]\dfrac{1}{3x}[/tex] will not be defined.
Hence, the value of x is:
3
