How do you solve #\frac { 5} { x + 2} - \frac { 3} { x } = 0#?

Question

Ethan Adkins · Accepted Answer

#x=3#

#frac{5}{x+2}-3/x=0#

Rewrite the second sentence to include a negative.

#frac{5}{x+2}+(-3)/x=0#

Multiply through by the common denominator #color(red)(x(x+2))#

#color(red)(x(x+2))xxfrac{5}{x+2} + color(red)(x(x+2)) xx frac{-3}{x} = color(red)(x(x+2)) xx 0#

#x(cancel(x+2)) xx 5/cancel(x+2) + cancel(x)(x+2) xx (-3)/cancel(x) =0#

#5x + -3(x+2) =0color(white)(aaa)#Distribute the -3

#5x-3x-6=0 color(white)(aaa)#Combine like terms

#2x-6=0#

#color(white)(aa) +6color(white)(a)+6color(white)(aaa)#Add 6 to both sides

#(2x)/2=6/2color(white)(aaa)#Divide by 2

#x=3#

It's usually a good idea to double-check your answers for extraneous solutions (those that divide by zero or don't work) when solving rational equations.

#5/(3+2) -3/3 = 0#

#color(white)(aaaaa)0=0#

Genesis Allen · Answer

undefined To solve the equation $\frac{5}{x + 2} - \frac{3}{x} = 0$, first, find a common denominator for the fractions, then combine them into a single fraction. Then, solve for $x$ by cross-multiplying and simplifying the resulting equation. Finally, solve for $x$ to find the value(s) that satisfy the equation.