Question 21 asks for the values of $x$ that make the expression $\frac{5x+3}{6x(x+1)}$ undefined. Question 22 asks us to express the product of their ages after four years in terms of the son's current age $y$, given that a man is five times as old as his son and the product of their ages in four years time is 340.

1. Problem Description

Question 21 asks for the values of $x$ that make the expression $\frac{5x+3}{6x(x+1)}$ undefined. Question 22 asks us to express the product of their ages after four years in terms of the son's current age $y$, given that a man is five times as old as his son and the product of their ages in four years time is

3

4

0.

2. Solution Steps

Question 21:

A rational expression is undefined when the denominator is equal to zero. So, we need to find the values of $x$ for which $6x(x+1) = 0$.

$6x(x+1) = 0$

This equation is satisfied when $x=0$ or $x+1=0$.

If $x=0$, the denominator is zero.

If $x+1=0$, then $x=-1$.

Therefore, the expression is undefined when $x=0$ or $x=-1$.

Question 22:

Let the son's age be $y$.

The man's age is $5y$.

In four years, the son's age will be $y+4$, and the man's age will be $5y+4$.

The product of their ages in four years is $(y+4)(5y+4) = 340$.

Expanding this equation:

$5y^2 + 4y + 20y + 16 = 340$

$5y^2 + 24y + 16 - 340 = 0$

$5y^2 + 24y - 324 = 0$

3. Final Answer

Question 21: B. {0, -1}

Question 22: D. $5y^2 + 24y - 324 = 0$