How do you solve #\frac { 4} { 5+ x } - \frac { 1} { x } = \frac { 1} { 4x }#?

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Answer 1 · 2018-01-25T16:46:15

#x = 25/11#

Let's add #1/x# to both sides.

#4/(5+x) - 1/x = 1/(4x)#

#4/(5+x) = 1/(4x) + 1/x#

We can combine the two fractions on the right pretty easily.

#4/(5+x) = 1/(4x) + 4/(4x)#

#4/(5+x) = 5/(4x)#

Now that we only have one fraction on each side, we can cross multiply and solve.

#4 * (4x) = 5 * (5+x)#

#16x = 25 + 5x#

#11x = 25#

#x = 25/11#

Final Answer