misswiss123
Solve the equation: 2/5 - 3/x = 1/(5x)
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gaara438125
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\[\frac{ 2 }{ 5 } - \frac{ 3 }{ x } = \frac{ 1 }{ 5x }\]
what's the LCD?
misswiss123
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I don't know
gaara438125
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\[\frac{ 2 }{ 3 } +\frac{ 7 }{ x } + \frac{ 32 }{ 6x }\]
the LCD would be 6x for all the denominators can multiply into 6x
3 * 2x | x * 6 | 6x * 1 |
gaara438125
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what ever you multiply the denominator by you HAVE to multiply the same number to the numerator.
misswiss123
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x=8 ?
gaara438125
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let's go back to the original equation and look at that in the denominator what is the highest number they can all equal? 5, x, and 5x
gaara438125
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lowest number*
misswiss123
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1?
gaara438125
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touche -.-" lol i meant without dividing 5, x and 5x can ALL equal 5x
misswiss123
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I have no idea ;'(
jim_thompson5910
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2/5 is equivalent to (2x)/(5x) if you multiply top and bottom by x
-3/x is equivalent to 15/(5x) if you multiply top and bottom by 5
Notice how they now have the same denominator of 5x
This means
2/5 - 3/x = 1/(5x)
is the same as
(2x)/(5x) - 15/(5x) = 1/(5x)
which allows you to combine the two fractions on the left side to get
(2x - 15)/(5x) = 1/(5x)
What's next?
jim_thompson5910
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any ideas?
misswiss123
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aaahhhhhh
jim_thompson5910
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yes? no?
jim_thompson5910
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If two fractions are equal, and their denominators are equal, then the numerators must be equal
jim_thompson5910
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so this means that if
(2x - 15)/(5x) = 1/(5x)
then
2x-15 = 1
jim_thompson5910
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if 2x - 15 = 1, then x = ???
misswiss123
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8?
jim_thompson5910
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you got it
misswiss123
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Thank youu