We have the equation:
#(x^2/(x+10)) - (10/(x+10)) = 0#
Left-hand side of the equation (LHS) is
#=(x^2/(x+10)) - (10/(x+10))#
To simplify LHS, take the common denominator which is #(x + 10)#
We get
#=(x^2 - 10)/(x+10)#
Now our equation becomes
# (x^2 - 10)/(x+10) = 0#
We can rewrite this equation as
# (x^2 - 10)/(x+10) = 0/0#
Multiply both sides by #(x+10)# to get
# (x + 10)(x^2 - 10)/(x+10) = (0/0)x+10#
#rArr x^2 - 10 = 0 " " color(red)(Equation.1)#
We can write 10 as #[ sqrt(10 )]^2#
Hence our #color(red)(Equation.1)# becomes
#rArr x^2 - (sqrt(10))^2 = 0 " " color(red)(Equation.2)#
We are now ready to use the factoring formula :
#(x^2 - y^2) = (x+y)(x-y) #
Now we can rewrite the #color(red)(Equation.2)# using our factoring formula as
#(x + sqrt(10)) (x - sqrt(10)) = 0 " " color(red)(Equation.3)#
We can get the factors as
#(x + sqrt(10)) =0 or (x - sqrt(10)) = 0#
#rArr x = -sqrt(10) or x = +sqrt(10)#
We get
#x= sqrt(10) = 3.16#;
#x = -sqrt(10) = -3.16#
I hope this is useful.
