Solve x/x+3/x*x-b=a-5x/sinx

$$\frac { x } { x } + \frac { 3 } { x } \cdot x - b = a - \frac { 5 x } { \sin x }$$

Solve for a (complex solution)

$$a=-\frac{i\left(-ib\sin(x)+4i\sin(x)+5ix\right)}{\sin(x)}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$x+3x-bx=xa-x\left(SinI(x)\right)^{-1}\times 5x$$

Combine x and 3x to get 4x.

$$4x-bx=xa-x\left(SinI(x)\right)^{-1}\times 5x$$

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

$$4x-bx=xa-x^{2}\left(SinI(x)\right)^{-1}\times 5$$

Swap sides so that all variable terms are on the left hand side.

$$xa-x^{2}\left(SinI(x)\right)^{-1}\times 5=4x-bx$$

Add x^{2}\left(SinI(x)\right)^{-1}\times 5 to both sides.

$$xa=4x-bx+x^{2}\left(SinI(x)\right)^{-1}\times 5$$

Reorder the terms.

$$ax=x\left(5x\times \frac{1}{\sin(x)}-b+4\right)$$

Express 5\times \frac{1}{\sin(x)} as a single fraction.

$$ax=x\left(\frac{5}{\sin(x)}x-b+4\right)$$

Use the distributive property to multiply x by \frac{5}{\sin(x)}x-b+4.

$$ax=\frac{5}{\sin(x)}x^{2}-xb+4x$$

Express \frac{5}{\sin(x)}x^{2} as a single fraction.

$$ax=\frac{5x^{2}}{\sin(x)}-xb+4x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -xb+4x times \frac{\sin(x)}{\sin(x)}.

$$ax=\frac{5x^{2}}{\sin(x)}+\frac{\left(-xb+4x\right)\sin(x)}{\sin(x)}$$

Since \frac{5x^{2}}{\sin(x)} and \frac{\left(-xb+4x\right)\sin(x)}{\sin(x)} have the same denominator, add them by adding their numerators.

$$ax=\frac{5x^{2}+\left(-xb+4x\right)\sin(x)}{\sin(x)}$$

Use the distributive property to multiply -xb+4x by \sin(x).

$$ax=\frac{5x^{2}-xb\sin(x)+4x\sin(x)}{\sin(x)}$$

The equation is in standard form.

$$xa=\frac{-bx\sin(x)+4x\sin(x)+5x^{2}}{\sin(x)}$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{x\left(\frac{5x}{\sin(x)}-b+4\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{x\left(\frac{5x}{\sin(x)}-b+4\right)}{x}$$

Divide x\left(-b+\frac{5x}{\sin(x)}+4\right) by x.

$$a=\frac{5x}{\sin(x)}-b+4$$

Solve for b (complex solution)

$$b=-\frac{i\left(-ia\sin(x)+4i\sin(x)+5ix\right)}{\sin(x)}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$x+3x-bx=xa-x\left(SinI(x)\right)^{-1}\times 5x$$

Combine x and 3x to get 4x.

$$4x-bx=xa-x\left(SinI(x)\right)^{-1}\times 5x$$

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

$$4x-bx=xa-x^{2}\left(SinI(x)\right)^{-1}\times 5$$

Subtract 4x from both sides.

$$-bx=xa-x^{2}\left(SinI(x)\right)^{-1}\times 5-4x$$

Reorder the terms.

$$-bx=-5x^{2}\times \frac{1}{\sin(x)}+ax-4x$$

Express -5\times \frac{1}{\sin(x)} as a single fraction.

$$-bx=\frac{-5}{\sin(x)}x^{2}+ax-4x$$

Express \frac{-5}{\sin(x)}x^{2} as a single fraction.

$$-bx=\frac{-5x^{2}}{\sin(x)}+ax-4x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply ax-4x times \frac{\sin(x)}{\sin(x)}.

$$-bx=\frac{-5x^{2}}{\sin(x)}+\frac{\left(ax-4x\right)\sin(x)}{\sin(x)}$$

Since \frac{-5x^{2}}{\sin(x)} and \frac{\left(ax-4x\right)\sin(x)}{\sin(x)} have the same denominator, add them by adding their numerators.

$$-bx=\frac{-5x^{2}+\left(ax-4x\right)\sin(x)}{\sin(x)}$$

Use the distributive property to multiply ax-4x by \sin(x).

$$-bx=\frac{-5x^{2}+ax\sin(x)-4x\sin(x)}{\sin(x)}$$

The equation is in standard form.

$$\left(-x\right)b=\frac{ax\sin(x)-4x\sin(x)-5x^{2}}{\sin(x)}$$

Divide both sides by -x.

$$\frac{\left(-x\right)b}{-x}=\frac{x\left(-\frac{5x}{\sin(x)}+a-4\right)}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$b=\frac{x\left(-\frac{5x}{\sin(x)}+a-4\right)}{-x}$$

Divide x\left(a-\frac{5x}{\sin(x)}-4\right) by -x.

$$b=\frac{5x}{\sin(x)}-a+4$$

Solve for a

$$a=\frac{5x}{\sin(x)}-b+4$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$x+3x-bx=xa-x\left(SinI(x)\right)^{-1}\times 5x$$

Combine x and 3x to get 4x.

$$4x-bx=xa-x\left(SinI(x)\right)^{-1}\times 5x$$

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

$$4x-bx=xa-x^{2}\left(SinI(x)\right)^{-1}\times 5$$

Swap sides so that all variable terms are on the left hand side.

$$xa-x^{2}\left(SinI(x)\right)^{-1}\times 5=4x-bx$$

Add x^{2}\left(SinI(x)\right)^{-1}\times 5 to both sides.

$$xa=4x-bx+x^{2}\left(SinI(x)\right)^{-1}\times 5$$

Reorder the terms.

$$ax=x\left(5x\times \frac{1}{\sin(x)}-b+4\right)$$

Express 5\times \frac{1}{\sin(x)} as a single fraction.

$$ax=x\left(\frac{5}{\sin(x)}x-b+4\right)$$

Use the distributive property to multiply x by \frac{5}{\sin(x)}x-b+4.

$$ax=\frac{5}{\sin(x)}x^{2}-xb+4x$$

Express \frac{5}{\sin(x)}x^{2} as a single fraction.

$$ax=\frac{5x^{2}}{\sin(x)}-xb+4x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -xb+4x times \frac{\sin(x)}{\sin(x)}.

$$ax=\frac{5x^{2}}{\sin(x)}+\frac{\left(-xb+4x\right)\sin(x)}{\sin(x)}$$

Since \frac{5x^{2}}{\sin(x)} and \frac{\left(-xb+4x\right)\sin(x)}{\sin(x)} have the same denominator, add them by adding their numerators.

$$ax=\frac{5x^{2}+\left(-xb+4x\right)\sin(x)}{\sin(x)}$$

Use the distributive property to multiply -xb+4x by \sin(x).

$$ax=\frac{5x^{2}-xb\sin(x)+4x\sin(x)}{\sin(x)}$$

The equation is in standard form.

$$xa=\frac{-bx\sin(x)+4x\sin(x)+5x^{2}}{\sin(x)}$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{x\left(\frac{5x}{\sin(x)}-b+4\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{x\left(\frac{5x}{\sin(x)}-b+4\right)}{x}$$

Divide x\left(-b+\frac{5x}{\sin(x)}+4\right) by x.

$$a=\frac{5x}{\sin(x)}-b+4$$

Solve for b

$$b=\frac{5x}{\sin(x)}-a+4$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$x+3x-bx=xa-x\left(SinI(x)\right)^{-1}\times 5x$$

Combine x and 3x to get 4x.

$$4x-bx=xa-x\left(SinI(x)\right)^{-1}\times 5x$$

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

$$4x-bx=xa-x^{2}\left(SinI(x)\right)^{-1}\times 5$$

Subtract 4x from both sides.

$$-bx=xa-x^{2}\left(SinI(x)\right)^{-1}\times 5-4x$$

Reorder the terms.

$$-bx=-5x^{2}\times \frac{1}{\sin(x)}+ax-4x$$

Express -5\times \frac{1}{\sin(x)} as a single fraction.

$$-bx=\frac{-5}{\sin(x)}x^{2}+ax-4x$$

Express \frac{-5}{\sin(x)}x^{2} as a single fraction.

$$-bx=\frac{-5x^{2}}{\sin(x)}+ax-4x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply ax-4x times \frac{\sin(x)}{\sin(x)}.

$$-bx=\frac{-5x^{2}}{\sin(x)}+\frac{\left(ax-4x\right)\sin(x)}{\sin(x)}$$

Since \frac{-5x^{2}}{\sin(x)} and \frac{\left(ax-4x\right)\sin(x)}{\sin(x)} have the same denominator, add them by adding their numerators.

$$-bx=\frac{-5x^{2}+\left(ax-4x\right)\sin(x)}{\sin(x)}$$

Use the distributive property to multiply ax-4x by \sin(x).

$$-bx=\frac{-5x^{2}+ax\sin(x)-4x\sin(x)}{\sin(x)}$$

The equation is in standard form.

$$\left(-x\right)b=\frac{ax\sin(x)-4x\sin(x)-5x^{2}}{\sin(x)}$$

Divide both sides by -x.

$$\frac{\left(-x\right)b}{-x}=\frac{x\left(-\frac{5x}{\sin(x)}+a-4\right)}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$b=\frac{x\left(-\frac{5x}{\sin(x)}+a-4\right)}{-x}$$

Divide x\left(a-\frac{5x}{\sin(x)}-4\right) by -x.

$$b=\frac{5x}{\sin(x)}-a+4$$