How do you solve #7/x+3/4=5/x#?

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Answer 1 · 2016-09-11T13:51:06

#x = - (8) / (3)#

We have: #(7) / (x) + (3) / (4) = (5) / (x)#

First, let's combine the fractions on the left-hand side of the equation:

#=> (28 + 3 x) / (4 x) = (5) / (x)#

Then, let's cross-multiply:

#=> x (28 + 3 x) = 5 (4 x)#

#=> 3 x^(2) + 28 x = 20 x#

Now, let's subtract #20 x# from both sides:

#=> 3 x^(2) + 8 x = 0#

We can factorise to get:

#=> x (3 x + 8) = 0#

#=> x = 0#

or

#=> 3 x + 8 = 0#

#=> 3 x = - 8#

#=> x = - (8) / (3)#

However, using #x = 0# in the original equation would yield undefined values.

Therefore, the only real solution to the equation is #x = - (8) / (3)#.