Solve 6x(23+16+1)*2/16=2*(23*2+6*2)/x+2*23+16/y

$$6 x \frac { ( 23 + 16 + 1 ) \times 2 } { 16 } = \frac { 2 \times ( 23 \times 2 + 6 \times 2 ) } { x } + \frac { 2 \times 23 + 16 } { y }$$

Solve for y (complex solution)

$$y=-\frac{31x}{58-15x^{2}}$$

$$x\neq 0\text{ and }x\neq -\frac{\sqrt{870}}{15}\text{ and }x\neq \frac{\sqrt{870}}{15}$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 16xy, the least common multiple of 16,x,y.

$$6xxy\left(23+16+1\right)\times 2=16y\times 2\left(23\times 2+6\times 2\right)+16x\left(2\times 23+16\right)$$

Multiply x and x to get x^{2}.

$$6x^{2}y\left(23+16+1\right)\times 2=16y\times 2\left(23\times 2+6\times 2\right)+16x\left(2\times 23+16\right)$$

Add 23 and 16 to get 39.

$$6x^{2}y\left(39+1\right)\times 2=16y\times 2\left(23\times 2+6\times 2\right)+16x\left(2\times 23+16\right)$$

Add 39 and 1 to get 40.

$$6x^{2}y\times 40\times 2=16y\times 2\left(23\times 2+6\times 2\right)+16x\left(2\times 23+16\right)$$

Multiply 6 and 40 to get 240.

$$240x^{2}y\times 2=16y\times 2\left(23\times 2+6\times 2\right)+16x\left(2\times 23+16\right)$$

Multiply 240 and 2 to get 480.

$$480x^{2}y=16y\times 2\left(23\times 2+6\times 2\right)+16x\left(2\times 23+16\right)$$

Multiply 16 and 2 to get 32.

$$480x^{2}y=32y\left(23\times 2+6\times 2\right)+16x\left(2\times 23+16\right)$$

Do the multiplications.

$$480x^{2}y=32y\left(46+12\right)+16x\left(2\times 23+16\right)$$

Add 46 and 12 to get 58.

$$480x^{2}y=32y\times 58+16x\left(2\times 23+16\right)$$

Multiply 32 and 58 to get 1856.

$$480x^{2}y=1856y+16x\left(2\times 23+16\right)$$

Multiply 2 and 23 to get 46.

$$480x^{2}y=1856y+16x\left(46+16\right)$$

Add 46 and 16 to get 62.

$$480x^{2}y=1856y+16x\times 62$$

Multiply 16 and 62 to get 992.

$$480x^{2}y=1856y+992x$$

Subtract 1856y from both sides.

$$480x^{2}y-1856y=992x$$

Combine all terms containing y.

$$\left(480x^{2}-1856\right)y=992x$$

Divide both sides by 480x^{2}-1856.

$$\frac{\left(480x^{2}-1856\right)y}{480x^{2}-1856}=\frac{992x}{480x^{2}-1856}$$

Dividing by 480x^{2}-1856 undoes the multiplication by 480x^{2}-1856.

$$y=\frac{992x}{480x^{2}-1856}$$

Divide 992x by 480x^{2}-1856.

$$y=\frac{31x}{15x^{2}-58}$$

Variable y cannot be equal to 0.

$$y=\frac{31x}{15x^{2}-58}\text{, }y\neq 0$$

Solve for y

$$y=-\frac{31x}{58-15x^{2}}$$

$$x\neq 0\text{ and }|x|\neq \frac{\sqrt{870}}{15}$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 16xy, the least common multiple of 16,x,y.

$$6xxy\left(23+16+1\right)\times 2=16y\times 2\left(23\times 2+6\times 2\right)+16x\left(2\times 23+16\right)$$

Multiply x and x to get x^{2}.

$$6x^{2}y\left(23+16+1\right)\times 2=16y\times 2\left(23\times 2+6\times 2\right)+16x\left(2\times 23+16\right)$$

Add 23 and 16 to get 39.

$$6x^{2}y\left(39+1\right)\times 2=16y\times 2\left(23\times 2+6\times 2\right)+16x\left(2\times 23+16\right)$$

Add 39 and 1 to get 40.

$$6x^{2}y\times 40\times 2=16y\times 2\left(23\times 2+6\times 2\right)+16x\left(2\times 23+16\right)$$

Multiply 6 and 40 to get 240.

$$240x^{2}y\times 2=16y\times 2\left(23\times 2+6\times 2\right)+16x\left(2\times 23+16\right)$$

Multiply 240 and 2 to get 480.

$$480x^{2}y=16y\times 2\left(23\times 2+6\times 2\right)+16x\left(2\times 23+16\right)$$

Multiply 16 and 2 to get 32.

$$480x^{2}y=32y\left(23\times 2+6\times 2\right)+16x\left(2\times 23+16\right)$$

Do the multiplications.

$$480x^{2}y=32y\left(46+12\right)+16x\left(2\times 23+16\right)$$

Add 46 and 12 to get 58.

$$480x^{2}y=32y\times 58+16x\left(2\times 23+16\right)$$

Multiply 32 and 58 to get 1856.

$$480x^{2}y=1856y+16x\left(2\times 23+16\right)$$

Multiply 2 and 23 to get 46.

$$480x^{2}y=1856y+16x\left(46+16\right)$$

Add 46 and 16 to get 62.

$$480x^{2}y=1856y+16x\times 62$$

Multiply 16 and 62 to get 992.

$$480x^{2}y=1856y+992x$$

Subtract 1856y from both sides.

$$480x^{2}y-1856y=992x$$

Combine all terms containing y.

$$\left(480x^{2}-1856\right)y=992x$$

Divide both sides by 480x^{2}-1856.

$$\frac{\left(480x^{2}-1856\right)y}{480x^{2}-1856}=\frac{992x}{480x^{2}-1856}$$

Dividing by 480x^{2}-1856 undoes the multiplication by 480x^{2}-1856.

$$y=\frac{992x}{480x^{2}-1856}$$

Divide 992x by 480x^{2}-1856.

$$y=\frac{31x}{15x^{2}-58}$$

Variable y cannot be equal to 0.

$$y=\frac{31x}{15x^{2}-58}\text{, }y\neq 0$$

Solve for x

$$x=\frac{\sqrt{3480y^{2}+961}+31}{30y}$$

$$x=\frac{-\sqrt{3480y^{2}+961}+31}{30y}\text{, }y\neq 0$$