Solve 3-x/5=1/x+3quad{l}{text{nessan}}{text{a)}20%}

$$\frac { 3 - x } { 5 } = \frac { 1 } { x + 3 } \quad \left. \begin{array} { l } { \text { nessan } } \\ { \text { a) } 20 \% } \end{array} \right.$$

Solve for x

$$x=2$$

$$x=-2$$

Steps by Finding Square Root

Variable x cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by 5\left(x+3\right), the least common multiple of 5,x+3.

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

Consider \left(x+3\right)\left(3-x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$9-x^{2}=5$$

Subtract 9 from both sides.

$$-x^{2}=5-9$$

Subtract 9 from 5 to get -4.

$$-x^{2}=-4$$

Divide both sides by -1.

$$x^{2}=\frac{-4}{-1}$$

Fraction \frac{-4}{-1} can be simplified to 4 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=4$$

Take the square root of both sides of the equation.

$$x=2 x=-2$$

Steps Using the Quadratic Formula

Variable x cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by 5\left(x+3\right), the least common multiple of 5,x+3.

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

Consider \left(x+3\right)\left(3-x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$9-x^{2}=5$$

Subtract 5 from both sides.

$$9-x^{2}-5=0$$

Subtract 5 from 9 to get 4.

$$4-x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-x^{2}+4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 4}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 4}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 4}}{2\left(-1\right)}$$

Multiply 4 times 4.

$$x=\frac{0±\sqrt{16}}{2\left(-1\right)}$$

Take the square root of 16.

$$x=\frac{0±4}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±4}{-2}$$

Now solve the equation x=\frac{0±4}{-2} when ± is plus. Divide 4 by -2.

$$x=-2$$

Now solve the equation x=\frac{0±4}{-2} when ± is minus. Divide -4 by -2.

$$x=2$$

The equation is now solved.

$$x=-2 x=2$$