Question

add the following expressions​

Answer 1

Answer:

$\frac{7}{15}x$ and $\frac{5x^2}{2}$

Step-by-step explanation:

(i)

$\frac{2}{5}x+\frac{2}{3}x+\frac{-4}{5}x$

First of all lets make their denominators equal. Here, LCM of denominators is 15 so, to make denominators 15

$(\frac{3}{5}x\times \frac{3}{3})+(\frac{2}{3}x\times \frac{5}{5})+(\frac{-4}{5}x\times \frac{3}{3})$

$=\frac{9}{15}x+\frac{10}{15}x+\frac{-12}{15}$

$=\frac{9x+10x-12x}{15}$

$=\frac{7x}{15} or \frac{7}{15}x$

(ii)

$\frac{3}{4}x^2 +5x^2 +(-3x^2)+(-\frac{1}{4}x^2)$

LCM of denominators is 4. Lets make the denominators of each term equal

$\frac{3}{4}x^2 +(5x^2\times \frac{4}{4}) +(-3x^2\times \frac{4}{4})+(-\frac{1}{4}x^2)$

=$\frac{3}{4}x^2 +\frac{20}{4}x^2 +\frac{-12}{4}x^2+(-\frac{1}{4}x^2)$

$=\frac{3x^2+20x^2-12x^2-x^2}{4}$

$=\frac{10x^2}{4}=\frac{5x^2}{2}$