12 Solve the equation (5)/(x+2)+(3)/(x^2)+2x=2 Show clear algebraic working.

Question

Answer 1

To solve the given equation

multiply both sides by \((x+2)(x^2+2x)\) to clear the fractions:

Next, expand the brackets and simplify the result:

This simplifies to:

Rearrange the equation, since it's a cubic equation:

And then, group the terms:

This simplifies further into the form of:

Setting each part of equation to zero, we get:

This gives us

, which does not solve our original equation (need to ensure the original denominators don't lead to division by zero), and

This gives us

.Solving the two valid exponential equations now:

and

.We get solutions for first

(ignore

since denominator term

generate division by zero) and for second solution

, not valid again for same reason. And so, Conclusion: The fall through solution for valid

is

from

and expression-wise its

. Have ensured original denominator doesn't cause division by zero issue.

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