Question

Solve for x algebraically; (2/3x)+(4/x)=(7/(x+1))

Answer 1

$\frac{2}{3x} + \frac{4}{x} = \frac{7}{x+1} \\ \\x\neq 0 \ \ and \ \x+1\neq 0 \\ \\x\neq 0 \ \ and \ \x \neq -1$

$\frac{2 }{3x}+\frac{4}{x} = \frac{7}{x+1} \\\\\ \frac{2+12}{3x} = \frac{7}{x+1} \\ \\\frac{14}{3x} = \frac{7}{x+1}\\ \\14(x+1)=3x\cdot 7$

$14 x+14=21x \\ \\14=21x-14x \\ \\ 7x=14 \ \ /: 7 \\ \\x=2$
 

Answer 2

$\frac{2}{3x} + \frac{4}{x} = \frac{7}{x+1}$

$\frac{2}{3x} + \frac{12}{3x} = \frac{7}{x+1}$

$\frac{14}{3x} = \frac{7}{x+1}$

$Cross\ multiply :$

$14(x+1) = 7 \times 3x$

$14x+14 = 21x$

$14x-21x =-14$

$-7x =-14$

$x = \frac{-14}{-7}$

$\boxed{x=2}$