how do i solve this: ( 3/x-1 ) + 2/x =4

Question

matheducatormcg · Answer

do you mean
$$\frac{3}{x-1}+\frac{2}{x}=4$$

anonymous · Answer

yes

matheducatormcg · Answer

these types of equations can be solved by finding the LCD of all the fractions and multiplying each fraction by that LCD.  The LCD  will divide out the denominator leaving you a much easier equation.

the LCD for these fractions is 
$$x(x-1)$$

matheducatormcg · Answer

so,
$$x(x-1)\left( \frac{3}{x-1} \right)+x(x-1)\left( \frac{2}{x} \right)=4x(x-1)$$

matheducatormcg · Answer

you need to distribute and solve for x now.  let me know if you need me to go further.

anonymous · Answer

so my new equation would be 2/x=4x-4 right?

matheducatormcg · Answer

not quite.
the first fraction has the x-1 divide out resulting in 3x
the next fraction has the x divide out resulting in 2(x-2), which is 2x-4
the other side of the equation becomes 4x^2-4x by the distributive property.

matheducatormcg · Answer

oops...
second fraction divided out to 2(x-1), which is 2x-2.
sorry about that

matheducatormcg · Answer

your new equation should look like
$$3x+2x-2=4x^2-4x$$

matheducatormcg · Answer

solve by factoring or quadratic formula now.

anonymous · Answer

okay