What causes a solution to a rational equation to be an extraneous solution?

Extraneous solution:

An extraneous solution is a solution that arises from the solving process that is not really a solution at all

So, firstly we will solve for the equation

and then we verify each solutions by plugging them back

If denominator of rational equation becomes zero , then that solution must be extraneuous solution

For example:

we can solve for x

Multiply both sides by x(x+3)

now, we can simplify it

now, we can solve for x

now, we can check whether x=-3 is extraneous solution

we will plug back x=-3 into original

we can see that denominator becomes 0

so, x=-3 can not be solution

so, x=-3 is extraneous solution...........Answer

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.