Studdy AI Logo
Math

QuestionSederhanakan m+6n2mn−m+3m\frac{m+6 n}{2 m n}-\frac{m+3}{m} menjadi satu pecahan tunggal yang paling sederhana.

Studdy Solution

STEP 1

Assumptions1. We are given the expression m+6nmn−m+3m\frac{m+6 n}{ m n}-\frac{m+3}{m}. . We are asked to express this as a single fraction in its simplest form.

STEP 2

To combine these two fractions, we need to find a common denominator. In this case, the common denominator is 2mn2mn.

STEP 3

We rewrite the second fraction with the common denominator. To do this, we multiply both the numerator and the denominator of the second fraction by 2n2n.
m+3m=(m+3)⋅2nm⋅2n\frac{m+3}{m} = \frac{(m+3) \cdot2n}{m \cdot2n}

STEP 4

implify the fraction.
m+3m=2mn+6n2mn\frac{m+3}{m} = \frac{2mn+6n}{2mn}

STEP 5

Now, we can subtract the two fractions as they have the same denominator.
m+n2mn−m+3m=m+n2mn−2mn+n2mn\frac{m+ n}{2 m n}-\frac{m+3}{m} = \frac{m+ n}{2 m n}-\frac{2mn+n}{2mn}

STEP 6

Subtract the numerators.
m+6n2mn−2mn+6n2mn=m+6n−2mn−6n2mn\frac{m+6 n}{2 m n}-\frac{2mn+6n}{2mn} = \frac{m+6n-2mn-6n}{2mn}

STEP 7

implify the numerator.
m+6n−2mn−6n2mn=m−2mn2mn\frac{m+6n-2mn-6n}{2mn} = \frac{m-2mn}{2mn}

STEP 8

Factor out mm in the numerator.
m−2mn2mn=m(1−2n)2mn\frac{m-2mn}{2mn} = \frac{m(1-2n)}{2mn}

STEP 9

implify the fraction.
m(−2n)2mn=−2n2n\frac{m(-2n)}{2mn} = \frac{-2n}{2n}So, m+6n2mn−m+3m\frac{m+6 n}{2 m n}-\frac{m+3}{m} simplifies to −2n2n\frac{-2n}{2n}.

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