Solve x+5/3+x-2=3(5x+1)-15x

$$\frac{ x+5 }{ 3+x } -2=3(5x+1)-15x$$

Solve for x

$$x = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by x+3.

$$x+5+\left(x+3\right)\left(-2\right)=3\left(5x+1\right)\left(x+3\right)-15x\left(x+3\right)$$

Use the distributive property to multiply x+3 by -2.

$$x+5-2x-6=3\left(5x+1\right)\left(x+3\right)-15x\left(x+3\right)$$

Combine x and -2x to get -x.

$$-x+5-6=3\left(5x+1\right)\left(x+3\right)-15x\left(x+3\right)$$

Subtract 6 from 5 to get -1.

$$-x-1=3\left(5x+1\right)\left(x+3\right)-15x\left(x+3\right)$$

Use the distributive property to multiply 3 by 5x+1.

$$-x-1=\left(15x+3\right)\left(x+3\right)-15x\left(x+3\right)$$

Use the distributive property to multiply 15x+3 by x+3 and combine like terms.

$$-x-1=15x^{2}+48x+9-15x\left(x+3\right)$$

Use the distributive property to multiply -15x by x+3.

$$-x-1=15x^{2}+48x+9-15x^{2}-45x$$

Combine 15x^{2} and -15x^{2} to get 0.

$$-x-1=48x+9-45x$$

Combine 48x and -45x to get 3x.

$$-x-1=3x+9$$

Subtract 3x from both sides.

$$-x-1-3x=9$$

Combine -x and -3x to get -4x.

$$-4x-1=9$$

Add 1 to both sides.

$$-4x=9+1$$

Add 9 and 1 to get 10.

$$-4x=10$$

Divide both sides by -4.

$$x=\frac{10}{-4}$$

Reduce the fraction \frac{10}{-4} to lowest terms by extracting and canceling out 2.

$$x=-\frac{5}{2}$$