How do you multiply #\frac { 7b + 35} { 7} \cdot \frac { b + 8} { b + 5}#?

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Jan 26, 2018

Answer:

See a solution process below:

Explanation:

First, factor the numerator of the fraction on the left as:

#((7 * b) + (7 * 5))/7 * (b + 8)/(b + 5) =>#

#(7(b + 5))/7 * (b + 8)/(b + 5)#

Next, cancel common terms in the numerators and denominators:

#(color(red)(cancel(color(black)(7)))color(blue)(cancel(color(black)((b + 5)))))/color(red)(cancel(color(black)(7))) * (b + 8)/color(blue)(cancel(color(black)(b + 5))) =>#

#1/1 * (b + 8)/1 =>#

#b + 8#

However, because we cannot divide by #0# we need to exclude where:

#b + 5 != 0#

Or

#b != -5#

So the solution is: #b + 8# where #b != -5#

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