Solve 1/3(2x+7)=x/(2x+7)(5-x)-5/(5-x)

$$\frac { 1 } { 3 ( 2 x + 7 ) } = \frac { x } { ( 2 x + 7 ) ( 5 - x ) } - \frac { 5 } { ( 5 - x ) }$$

Solve for x

$$x = -\frac{55}{13} = -4\frac{3}{13} \approx -4.230769231$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{7}{2},5 since division by zero is not defined. Multiply both sides of the equation by 3\left(x-5\right)\left(2x+7\right), the least common multiple of 3\left(2x+7\right),\left(2x+7\right)\left(5-x\right),5-x.

$$x-5=-3x-\left(-21-6x\right)\times 5$$

Use the distributive property to multiply -21-6x by 5.

$$x-5=-3x-\left(-105-30x\right)$$

To find the opposite of -105-30x, find the opposite of each term.

$$x-5=-3x+105+30x$$

Combine -3x and 30x to get 27x.

$$x-5=27x+105$$

Subtract 27x from both sides.

$$x-5-27x=105$$

Combine x and -27x to get -26x.

$$-26x-5=105$$

Add 5 to both sides.

$$-26x=105+5$$

Add 105 and 5 to get 110.

$$-26x=110$$

Divide both sides by -26.

$$x=\frac{110}{-26}$$

Reduce the fraction \frac{110}{-26} to lowest terms by extracting and canceling out 2.

$$x=-\frac{55}{13}$$