Extracting good from within sin

בהפטורה דשובה תשא עון וקח טוב.

In the Haftarah of Shuvah: "Forgive iniquity and accept good" (Hoshea 14:3).

The Sefas Emes draws on the Haftarah of Shabbos Shuvah, where the navi pairs the forgiving of sin with the taking of "good."

כי בכל דבר יש תערובות טו"ר וצריכין לשוב לבער הפסולת ולהוציא הנק"ד שנתערבו בהחטא.

For in everything there is a mixture of good and evil (tov v'ra), and one must do teshuvah to burn away the dross and extract the holy point that has become intermingled within the sin.

Every act and object holds a blend of good and evil; teshuvah is the work of separating out the holy nekudah (inner point) trapped even inside the aveirah and discarding the worthless remainder.

וזהו למדו הטיב להטיב כדפרש"י שם.

And this is the meaning of "Learn to do good" (Yeshayahu 1:17), as Rashi explains there.

The verse "learn to do good" teaches that doing good is itself a learned skill — the avodah of extracting good, as Rashi indicates.

וע"י התורה שנקראת לקח טוב יכולין למצוא טוב הגנוז ונסתר גם בתוך החטא עצמו.

And through the Torah, which is called "good takings" (lekach tov), one is able to find the good that is hidden and concealed even within the sin itself.

The Torah, called "a good acquisition" (Mishlei 4:2), is the instrument that lets a person locate the buried good even inside the aveirah itself.

וז"ש הקב"ה לקין אם תטיב שאת.

And this is what Hashem said to Kayin: "If you do good, there is uplifting" (Bereishis 4:7).

Hashem's words to Kayin — "if you better yourself, you will be lifted up" — point to this very power of drawing out the good and elevating it.

וכמו שאין אדם חוטא אא"כ נכנס בו רוח שטות שהוא תערובת הרע כמו כן א"י לשוב רק כשזוכין לרוח טהרה מתוך התורה.

And just as a person does not sin unless a spirit of folly (ruach shtus) — which is the admixture of evil — enters into him, so too he cannot do teshuvah except when he merits a spirit of purity (ruach taharah) drawn from within the Torah.

Chazal say no one sins unless a ruach shtus enters him; the Sefas Emes mirrors this — teshuvah likewise requires a ruach taharah, and that pure spirit is accessed specifically through the Torah.

ואז זה הטוב מעביר הפסולת ויוכל להוציא טוב הגנוז:

And then this good removes the dross, and one is able to extract the hidden good.

Once the ruach taharah of Torah is present, it burns off the worthless dross and frees the concealed good that had been mixed into the sin.

Summary: Every act contains a mixture of good and evil; teshuvah — empowered by the ruach taharah that comes from the Torah ("lekach tov") — is the work of burning away the dross and drawing out the holy point of good hidden even inside the sin itself.