Answer:
MN = x(x + 1)/(x + 3)
Step-by-step explanation:
We are given;
MN/LN = PN/QN
From the diagram;
Let MN = y
LN = x + 1 + y
PN = x
QN = x + 3 + x = 2x + 3
Thus;
y/(x + y + 1) = x/(2x + 3)
Rearranging gives;
y(2x + 3) = x(x + y + 1)
2xy + 3y = x² + xy + x
x² + x = xy + 3y
x(x + 1) = y(x + 3)
y = x(x + 1)/(x + 3)
Thus; MN = x(x + 1)/(x + 3)
