Solve x+3/x=3x+5/5quadb)

$$\frac { x + 3 } { x } = \frac { 3 x + 5 } { 5 } \quad b )$$

Solve for b

$$b=\frac{5\left(x+3\right)}{x\left(3x+5\right)}$$

$$x\neq -\frac{5}{3}\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5x, the least common multiple of x,5.

$$5\left(x+3\right)=x\left(3x+5\right)b$$

Use the distributive property to multiply 5 by x+3.

$$5x+15=x\left(3x+5\right)b$$

Use the distributive property to multiply x by 3x+5.

$$5x+15=\left(3x^{2}+5x\right)b$$

Use the distributive property to multiply 3x^{2}+5x by b.

$$5x+15=3x^{2}b+5xb$$

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

$$3x^{2}b+5xb=5x+15$$

Combine all terms containing b.

$$\left(3x^{2}+5x\right)b=5x+15$$

Divide both sides by 3x^{2}+5x.

$$\frac{\left(3x^{2}+5x\right)b}{3x^{2}+5x}=\frac{5x+15}{3x^{2}+5x}$$

Dividing by 3x^{2}+5x undoes the multiplication by 3x^{2}+5x.

$$b=\frac{5x+15}{3x^{2}+5x}$$

Divide 15+5x by 3x^{2}+5x.

$$b=\frac{5\left(x+3\right)}{x\left(3x+5\right)}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{\sqrt{5\left(b+5\right)\left(5b+1\right)}+5b-5}{6b}\text{; }x=-\frac{-\sqrt{5\left(b+5\right)\left(5b+1\right)}+5b-5}{6b}\text{, }&b\neq 0\\x=-3\text{, }&b=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{\sqrt{5\left(b+5\right)\left(5b+1\right)}+5b-5}{6b}\text{; }x=-\frac{-\sqrt{5\left(b+5\right)\left(5b+1\right)}+5b-5}{6b}\text{, }&\left(b\neq 0\text{ and }b\geq -\frac{1}{5}\right)\text{ or }b\leq -5\\x=-3\text{, }&b=0\end{matrix}\right.$$