Solve 5/x+frac{2sqrt{3}}{43}=4+6sqrt{3}

$$\frac { 5 } { x } + \frac { 2 \sqrt { 3 } } { 43 } = 4 + 6 \sqrt { 3 }$$

Solve for x

$$x=\frac{3440\sqrt{3}}{10439}-\frac{9245}{41756}\approx 0.349363424$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 43x, the least common multiple of x,43.

$$43\times 5+x\times 2\sqrt{3}=43x\times 4+6\sqrt{3}\times 43x$$

Multiply 43 and 5 to get 215.

$$215+x\times 2\sqrt{3}=43x\times 4+6\sqrt{3}\times 43x$$

Multiply 43 and 4 to get 172.

$$215+x\times 2\sqrt{3}=172x+6\sqrt{3}\times 43x$$

Multiply 6 and 43 to get 258.

$$215+x\times 2\sqrt{3}=172x+258\sqrt{3}x$$

Subtract 172x from both sides.

$$215+x\times 2\sqrt{3}-172x=258\sqrt{3}x$$

Subtract 258\sqrt{3}x from both sides.

$$215+x\times 2\sqrt{3}-172x-258\sqrt{3}x=0$$

Combine x\times 2\sqrt{3} and -258\sqrt{3}x to get -256x\sqrt{3}.

$$215-256x\sqrt{3}-172x=0$$

Subtract 215 from both sides. Anything subtracted from zero gives its negation.

$$-256x\sqrt{3}-172x=-215$$

Combine all terms containing x.

$$\left(-256\sqrt{3}-172\right)x=-215$$

Divide both sides by -256\sqrt{3}-172.

$$\frac{\left(-256\sqrt{3}-172\right)x}{-256\sqrt{3}-172}=-\frac{215}{-256\sqrt{3}-172}$$

Dividing by -256\sqrt{3}-172 undoes the multiplication by -256\sqrt{3}-172.

$$x=-\frac{215}{-256\sqrt{3}-172}$$

Divide -215 by -256\sqrt{3}-172.

$$x=\frac{3440\sqrt{3}}{10439}-\frac{9245}{41756}$$