How do you evaluate #\frac { 4} { x ^ { 2} - 25} + \frac { 6} { x ^ { 2} + 6x + 5}#?
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"How does a vector quantity differ from a scalar quantity?"
- Factor the denominators
- Find LCD
- Make equivalent fractions with Like denominators
- Add like Terms
#(10x - 26)/((x-5)(x+5)(x+1) )#
#4/(x^2 -25) + 6/(x^2 + 6x +5) #
to factor #x^2-25# you need to understand difference of squares where #(x-5)(x+5) = x^2 -25#
#4/((x-5)(x+5)) + 6/((x+1)(x+5)#
our LCD is #(x-5)(x+5)(x+1) #
#4/((x-5)(x+5)) * ((x+1))/((x+1)) = (4(x+1))/((x-5)(x+5)(x+1)# and
#6/((x+1)(x+5)) * ((x-5))/((x-5)) = (6(x-5))/((x-5)(x+5)(x+1))#
#(4(x+1) + 6(x-5))/((x-5)(x+5)(x+1) )#
Distributive Property
#(4x + 4 + 6x - 30)/((x-5)(x+5)(x+1) )#
add like terms
#(10x - 26)/((x-5)(x+5)(x+1) )# Fully simplified
