What does side LN equal?

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)

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