Solve the equation for (6x)/(7)-(x+1)/(3)=(x+1)/(4) Write your answer as a fraction x=square

To solve the equation, we first find a common denominator for the fractions on the left side of the equation, which is 21. This gives us:<br /><br />$\frac{6x}{7} - \frac{x+1}{3} = \frac{x+1}{4}$<br /><br />$\frac{18x}{21} - \frac{7(x+1)}{21} = \frac{7(x+1)}{28}$<br /><br />Simplifying the equation, we get:<br /><br />$\frac{11x}{21} = \frac{7(x+1)}{28}$<br /><br />Cross-multiplying, we have:<br /><br />$28 \cdot 11x = 7 \cdot 21(x+1)$<br /><br />$308x = 147(x+1)$<br /><br />Expanding and simplifying, we get:<br /><br />$308x = 147x + 147$<br /><br />$161x = 147$<br /><br />$x = \frac{147}{161}$<br /><br />Therefore, the solution to the equation is $x = \frac{147}{161}$.