Question

(x/2-y/3) (x/2-y/3+1)​

Answer 1

GIVEN:

$\bold{ (\frac{x}{2} - \frac{y}{3})( \frac{x}{2} - \frac{y}{3} + 1) }$

FIND:

$\bold{solve \: the \: expression (\frac{x}{2} - \frac{y}{3})( \frac{x}{2} - \frac{y}{3} + 1) }$

SOLUTION:

We have,

$\bold{ \to (\frac{x}{2} - \frac{y}{3})( \frac{x}{2} - \frac{y}{3} + 1) }$

$\bold{multiply \: the \: parentheses}$

$\huge{ \bold{ \downarrow \downarrow \downarrow \downarrow }}$

$\bold{ \to \red{ \frac{x}{2} \times ( \frac{x}{2} - \frac{y}{3} + 1) - \frac{y}{3} ( \frac{x}{2} - \frac{y}{3} + 1) }}$

$\bold{now \: take \: the \: lcm}$

$\huge{ \bold{ \downarrow \downarrow \downarrow \downarrow }}$

$\bold{ \to \frac{x}{2} \times \red{\frac{3x - 2y + 6}{6}} -\frac{y}{3} \times \red{\frac{3x - 2y + 6}{6} }}$

$\bold{multiply \: the \: fraction}$

$\huge{ \bold{ \downarrow \downarrow \downarrow \downarrow }}$

$\bold{ \to \red{\frac{x \times (3x - 2y + 6)}{12}} - \red{\frac{y \times (3x - 2y + 6)}{18} }}$

$\bold{ \underline{ \orange{distribute}} \: x \: and \: y\: through \: the \: parantheses}$

$\huge{ \bold{ \downarrow \downarrow \downarrow \downarrow }}$

$\bold{ \to \red{\frac{( {3x}^{2} - 2xy + 6x)}{12}} - \red{ \frac{(3x - {2y}^{2} + 6y)}{18} }}$

$\bold{again\: take \: the \: lcm}$

$\huge{ \bold{ \downarrow \downarrow \downarrow \downarrow }}$

$\bold{ \to \frac{3( {3x}^{2} - 2xy + 6x) - 2(3x - {2y}^{2} + 6y)}{36}}$

$\bold{ \to \frac{{9x}^{2} - 6xy + 18x - 6xy + {4y}^{2} - 12y}{36}}$

$\bold{collect \: like \: terms}$

$\huge{ \bold{ \downarrow \downarrow \downarrow \downarrow }}$

$\bold{ \to \frac{{9x}^{2} - 12xy + 18x + {4y}^{2} - 12y}{36}}$

Hence, ANSWER

$\bold{ \longrightarrow \frac{{9x}^{2} - 12xy + 18x + {4y}^{2} - 12y}{36}}$

Answer 2

$\huge\bold\blue{Answer!}$

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number.