How do you simplify #\frac { 4} { 3} + \frac { 5} { 2x + 6}#?

Question

Hazel Anglin · Accepted Answer

#(8x+39)/(3(2x+6))#

we need to put it over a common denominator; the simplest way to achieve this is to follow the 'cross multiplication method'

#color(red)(a)/color(blue)(b)+-color(blue)(c)/color(red)d=(color(red)(ad)+-color(blue)(bc))/color(blue)(bcolor(red)(d))#

#4/3+5/(2x+6)#

#=(4(2x+6)+(3xx5))/(3(2x+6))#

now we simplify

#=(8x+24+15)/(3(2x+6)#

#(8x+39)/(3(2x+6))#

usually we leave the denominator factorised

Jace Anderson · Answer

undefined To simplify the expression $ \frac{4}{3} + \frac{5}{2x + 6} $, you first need to find a common denominator for both fractions. In this case, the least common denominator is $3(2x + 6)$, which is the least common multiple of 3 and $2x + 6$.

Now, rewrite each fraction with the common denominator:

$$ \frac{4}{3} + \frac{5}{2x + 6} = \frac{4(2x + 6)}{3(2x + 6)} + \frac{5(3)}{3(2x + 6)} $$

Next, simplify each fraction:

$$ = \frac{8x + 24}{3(2x + 6)} + \frac{15}{3(2x + 6)} $$

Now that both fractions have the same denominator, you can combine them:

$$ = \frac{(8x + 24) + 15}{3(2x + 6)} $$

$$ = \frac{8x + 24 + 15}{3(2x + 6)} $$

$$ = \frac{8x + 39}{3(2x + 6)} $$

So, $ \frac{4}{3} + \frac{5}{2x + 6} $ simplifies to $ \frac{8x + 39}{3(2x + 6)} $.