Question
Simplify. Express your answer as a single fraction in simplest form.
a+10–
a
a2–40a+49
a+10–
a
a2–40a+49
Answers
GPT-4o mini
To simplify the expression \( \frac{a+10-a}{a^2 - 40a + 49} \), we first combine the terms in the numerator:
\[
a + 10 - a = 10.
\]
Next, we need to factor the denominator, \( a^2 - 40a + 49 \). We can attempt to factor it as a quadratic expression. To do this, we look for two numbers that multiply to \( 49 \) and add up to \( -40 \). The quadratic can be factored as follows:
\[
a^2 - 40a + 49 = (a - 1)(a - 39).
\]
Now the expression becomes:
\[
\frac{10}{(a - 1)(a - 39)}.
\]
Therefore, the simplified expression in its simplest form is:
\[
\boxed{\frac{10}{(a - 1)(a - 39)}}.
\]
\[
a + 10 - a = 10.
\]
Next, we need to factor the denominator, \( a^2 - 40a + 49 \). We can attempt to factor it as a quadratic expression. To do this, we look for two numbers that multiply to \( 49 \) and add up to \( -40 \). The quadratic can be factored as follows:
\[
a^2 - 40a + 49 = (a - 1)(a - 39).
\]
Now the expression becomes:
\[
\frac{10}{(a - 1)(a - 39)}.
\]
Therefore, the simplified expression in its simplest form is:
\[
\boxed{\frac{10}{(a - 1)(a - 39)}}.
\]