Question

Can someone please explain how to solve these 3 problems? It says “simplify the following fractions”

Answer 1

When adding fractions, you must express them over a common denominator. The easiest common denominator to find is the product of the denominators of the individual fractions. That is ...

`\displaystyle(a)/(b)+(c)/(d)=(ad+bc)/(bd)`

When dividing fractions, multiply by the inverse of the denominator fraction.

`\displaystyle(\left((a)/(b)\right))/(\left((c)/(d)\right))=(a)/(b)\cdot(d)/(c)=(ad)/(bc)`

12.

`\displaystyle((2)/(x)-3)/(1-(1)/(x-1))=((2-3x)/(x))/((x-1-1)/(x-1))\\\\=((2-3x)(x-1))/(x(x-2))=(-3x^2+5x-2)/(x^2-2x)`

13.

`\displaystyle((1)/(x^2)-(1)/(y^2))/((1)/(x)+(1)/(y))=((y^2-x^2)/(x^(2)y^(2)))/((y+x)/(xy))\\\\=(\left(y^2-x^2\right)xy)/((y+x)x^(2)y^(2))=((y-x)(y+x))/((y+x)xy)=(y-x)/(xy)`

14.

`\displaystyle((x)/(2)-1)/(x-2)=((x-2)/(2))/(x-2)=(x-2)/(2)\cdot(1)/(x-2)=(1)/(2)`