How do you find the quotient of #(14x^2+7x)div7x#?

2 Answers
Jun 17, 2017

Answer:

#2x +1#

Explanation:

You can compare this to

#3x(5x+4) = 15x^2 +12x#

where the #" "3x" "# is multiplied by both terms inside the bracket using the distributive law,

#(14x^2 +7x)div 7x" "# can be written as #" "1/(7x)(14x^2 +7x)#

Or as #" "(14x^2 +7x)/(7x)#

Or as separate terms: #" "(14x^2)/(7x) +(7x)/(7x)#

Whichever you choose, each of the terms has to be divided by #7x#

#=2x +1#

Jun 17, 2017

Answer:

See a solution process below:

Explanation:

First, rewrite the expression as:

#(14x^2 + 7x)/(7x) => (14x^2)/(7x) + (7x)/(7x) => (14x^2)/(7x) + 1#

Next, factor #7x# out of the numerator and denominator in the fraction on the left giving:

#(7x xx 2x)/(7x xx 1) + 1 => (color(red)(cancel(color(black)(7x))) xx 2x)/(color(red)(cancel(color(black)(7x))) xx 1) + 1 => (2x)/1 + 1 =>#

#2x + 1#

However, from the original expression we cannot divide by #0# therefore we need the exclusion:

Where: #7x != 0# or #x != 0#