How do you solve #6+ \frac { 1} { x - 1} = - \frac { 6} { x - 2}#?
1 Answer
Ultimately, you're solving for
Explanation:
Solving implies we determine the value of the variable. To do this, we must isolate and solve for
#6 + 1/(x-1) = 6/(x-2)#
Before we do that, let's simplify the left side. To do this, let's make the
#[6xx (x-1)/(x-1) ] + 1/(x-1) = 6/(x-2)#
#(6(x-1))/(x-1) + 1/(x-1) = 6/(x-2)#
#(6x-6)/(x-1) + 1/(x-1) = 6/(x-2)#
Now we can add the two terms.
#(6x-6+1)/(x-1) = 6/(x-2)#
#(6x-5)/(x-1) = 6/(x-2)#
Now we can cross-multiply. Cross-multiplying is done by:
#(6x-5)(x-2)=(6)(x-1)#
Now we simplify both sides. On the left side, we have to expand the brackets.
#6x^2-12x-5x+10=6x-6#
#6x^2-17x+10=6x-6#
Now, we are going to bring the terms to one side and simplify again. We are also going to equate the expression to
#6x^2-17x+10-6x+6=0#
#6x^2-23x+16=0#
Now we are going to factor the equation. To avoid any complications, we will just use the quadratic formula.
Simplify.
Now we solve for
#x (+) ~~ 2.92#
#x (-) ~~ 0.91#
We can double check our work by graphing the function and finding the zeros.
Hope this helps :)