Solve 5/2p+3-3/p-2=4/2p+3

$$\frac { 5 } { 2 p + 3 } - \frac { 3 } { p - 2 } = \frac { 4 } { 2 p + 3 }$$

Solve for p

$$p = -\frac{11}{5} = -2\frac{1}{5} = -2.2$$

Steps for Solving Linear Equation

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

$$\left(p-2\right)\times 5-\left(2p+3\right)\times 3=\left(p-2\right)\times 4$$

Use the distributive property to multiply p-2 by 5.

$$5p-10-\left(2p+3\right)\times 3=\left(p-2\right)\times 4$$

Use the distributive property to multiply 2p+3 by 3.

$$5p-10-\left(6p+9\right)=\left(p-2\right)\times 4$$

To find the opposite of 6p+9, find the opposite of each term.

$$5p-10-6p-9=\left(p-2\right)\times 4$$

Combine 5p and -6p to get -p.

$$-p-10-9=\left(p-2\right)\times 4$$

Subtract 9 from -10 to get -19.

$$-p-19=\left(p-2\right)\times 4$$

Use the distributive property to multiply p-2 by 4.

$$-p-19=4p-8$$

Subtract 4p from both sides.

$$-p-19-4p=-8$$

Combine -p and -4p to get -5p.

$$-5p-19=-8$$

Add 19 to both sides.

$$-5p=-8+19$$

Add -8 and 19 to get 11.

$$-5p=11$$

Divide both sides by -5.

$$p=\frac{11}{-5}$$

Fraction \frac{11}{-5} can be rewritten as -\frac{11}{5} by extracting the negative sign.

$$p=-\frac{11}{5}$$