Question 502053
4- a-5/a+3 = a^2-1/a+3 
since denominators are equal, the numerators are equal
a-5=a^2-1
a^2-a+4=0
you are correct, it is a quadratic equation
a=1, b=-1, c=4
but there is no real number solution because
the discriminate, (b^2-4ac)<0