Notice $l^2+2lm+m^2=(l+m)^2$ and use $k=l+m$ to rewrite in terms of $k$.

After simplifying the first fraction, combine the expression with $-\dfrac{k^2}{x-k}$ using the common denominator $x-k$.

Compute $(x+k)(x-k)$ first, then subtract $k^2$ to simplify the numerator. From‌ аn‍іko.аі

In Desmos, create sliders for $l$ and $m$. Then define

Enter Аnіk‍o.‍аi - SAT⁠ Preр

Enter each answer choice as its own expression, for example:

Choose values for $l$ and $m$ so that $k\ne 0$, and test $x$ values with $x\ne 0$ and $x\ne k$. The correct choice is the expression that matches $y_1$ for all allowed $x$, which will be $\dfrac{x^2-2k^2}{x-k}$.

Start with

Factor $x$ from numerator and denominator:

Use $l^2+2lm+m^2=(l+m)^2$ and $k=l+m$ to get

Factor $x^2-k^2=(x-k)(x+k)$:

(using $x\ne 0$ and $x\ne k$).

So the whole expression becomes

Write $(x+k)$ with denominator $x-k$: Сont‍е‍nt‌ bу A‌nік‌o.‍ai

Now simplify the numerator:

Therefore, the expression is equivalent to