How do you solve #(x - 1) ( x + 3+ \frac { 3} { x - 1} ) = ( \frac { 4- x } { x - 1} ) ( x - 1)#?

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Answer 1 · 2017-04-11T15:45:00

#x_1=-4#; #cancel(color(red)(x_2=1))#

You would multiply and simplify #x-1# and state that #color(red)(x!=1)#:

#x^2+3xcancel(-x)cancel(-3)cancel(+3)=4cancel(-x)#

that's

#x^2+3x-4=0#

#x=(-3+-sqrt(9+16))/2#

#x=(-3+-5)/2#

and the solutions are:

#x_1=-4#; #cancel(color(red)(x_2=1))#