Solve 1-5/2x+5=3/x+3

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

Solve for x

$$x = \frac{\sqrt{30}}{2} \approx 2.738612788$$

$$x = -\frac{\sqrt{30}}{2} \approx -2.738612788$$

Steps by Finding Square Root

Variable x cannot be equal to any of the values -3,-\frac{5}{2} since division by zero is not defined. Multiply both sides of the equation by \left(x+3\right)\left(2x+5\right), the least common multiple of 2x+5,x+3.

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

Use the distributive property to multiply x+3 by 2x+5 and combine like terms.

$$2x^{2}+11x+15-\left(x+3\right)\times 5=\left(2x+5\right)\times 3$$

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

$$2x^{2}+11x+15-\left(5x+15\right)=\left(2x+5\right)\times 3$$

To find the opposite of 5x+15, find the opposite of each term.

$$2x^{2}+11x+15-5x-15=\left(2x+5\right)\times 3$$

Combine 11x and -5x to get 6x.

$$2x^{2}+6x+15-15=\left(2x+5\right)\times 3$$

Subtract 15 from 15 to get 0.

$$2x^{2}+6x=\left(2x+5\right)\times 3$$

Use the distributive property to multiply 2x+5 by 3.

$$2x^{2}+6x=6x+15$$

Subtract 6x from both sides.

$$2x^{2}+6x-6x=15$$

Combine 6x and -6x to get 0.

$$2x^{2}=15$$

Divide both sides by 2.

$$x^{2}=\frac{15}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{30}}{2} x=-\frac{\sqrt{30}}{2}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to any of the values -3,-\frac{5}{2} since division by zero is not defined. Multiply both sides of the equation by \left(x+3\right)\left(2x+5\right), the least common multiple of 2x+5,x+3.

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

Use the distributive property to multiply x+3 by 2x+5 and combine like terms.

$$2x^{2}+11x+15-\left(x+3\right)\times 5=\left(2x+5\right)\times 3$$

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

$$2x^{2}+11x+15-\left(5x+15\right)=\left(2x+5\right)\times 3$$

To find the opposite of 5x+15, find the opposite of each term.

$$2x^{2}+11x+15-5x-15=\left(2x+5\right)\times 3$$

Combine 11x and -5x to get 6x.

$$2x^{2}+6x+15-15=\left(2x+5\right)\times 3$$

Subtract 15 from 15 to get 0.

$$2x^{2}+6x=\left(2x+5\right)\times 3$$

Use the distributive property to multiply 2x+5 by 3.

$$2x^{2}+6x=6x+15$$

Subtract 6x from both sides.

$$2x^{2}+6x-6x=15$$

Combine 6x and -6x to get 0.

$$2x^{2}=15$$

Subtract 15 from both sides.

$$2x^{2}-15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-15\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-15\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-15\right)}}{2\times 2}$$

Multiply -8 times -15.

$$x=\frac{0±\sqrt{120}}{2\times 2}$$

Take the square root of 120.

$$x=\frac{0±2\sqrt{30}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±2\sqrt{30}}{4}$$

Now solve the equation x=\frac{0±2\sqrt{30}}{4} when ± is plus.

$$x=\frac{\sqrt{30}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{30}}{4} when ± is minus.

$$x=-\frac{\sqrt{30}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{30}}{2} x=-\frac{\sqrt{30}}{2}$$