Math

QuestionSimplify the expression: x5x26x+5\frac{x-5}{x^{2}-6 x+5}.

Studdy Solution

STEP 1

Assumptions1. We are given the expression x5x6x+5\frac{x-5}{x^{}-6 x+5}. . We need to simplify this expression.

STEP 2

To simplify the expression, we need to factorize the denominator.
The quadratic equation x26x+5x^{2}-6 x+5 can be factorized into two binomial expressions.

STEP 3

Factorize the quadratic equation x26x+5x^{2}-6 x+5.
To do this, we need to find two numbers that multiply to5 (the constant term) and add to -6 (the coefficient of the x term).

STEP 4

The two numbers that satisfy these conditions are - and -1. Therefore, the factorization of the quadratic equation x26x+x^{2}-6 x+ is (x)(x1)(x-)(x-1).
x26x+=(x)(x1)x^{2}-6 x+ = (x-)(x-1)

STEP 5

Substitute the factorized form of the denominator back into the original expression.
x5x2x+5=x5(x5)(x1)\frac{x-5}{x^{2}- x+5} = \frac{x-5}{(x-5)(x-1)}

STEP 6

Now, we can cancel out the common factor (x5)(x-5) from the numerator and the denominator.
x5(x5)(x1)=1x1\frac{x-5}{(x-5)(x-1)} = \frac{1}{x-1}So, the simplified form of the given expression is 1x1\frac{1}{x-1}.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord