Tricks for manipulating this equation type.

#color(red)("Very important "->" What you do to one side of the equation you do to the other side.")#

#color(green)("To move an add or subtract to the other side of the = turn it into 0")#

#color(green)("To move a multiply or divide to the other side of the = turn it into 1")#

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Given:#" "(3/x)+(2/m)=(1/n)#

Write as:

#" "3/x+2/m=1/n#

We need to determine the value of #x# so we need to 'get rid' of #2/m# so that we have #3/x# on its own.

Subtract #color(blue)(2/m) " "underline("from both sides")#

#" "color(brown)(3/x+2/m color(blue)(-2/m)" "=" "1/n color(blue)(-2/m))#

#color(white)(.)#

#" "3/x+0=1/n-2/m#

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To do the next bit we need to combine #1/n-2/m#

Multiply #1/n# by 1 but in the form of #1=m/m#

Multiply #2/m# by 1 but in the form of #1=n/n#

#" "3/x=(1/nxxm/m)-(2/mxxn/n)#

#" "3/x=((1xxm)/(nxxm))-((2xxn)/(mxxn))#

#" "3/x=((m)/(mn))-((2n)/(mn))#

#" "3/x=(m-2n)/(mn)#

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Now you can turn everything upside down

#" "x/3=(mn)/(m-2n)#

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Multiply both sides by #color(blue)(" "3)#

#color(brown)(" "x xx(color(blue)(3))/3=(color(blue)(3)mn)/(m-2n))#

But #3/3 = 1# giving:

#" "x=(3mn)/(m-2n)#