m/n+9=m-4/m+1 eching

$$\frac { m } { n + 9 } = \frac { m - 4 } { m + 1 }$$

n uchun yechish

$$n=-\frac{m^{2}-8m+36}{4-m}$$

$$m\neq -1\text{ and }m\neq 0\text{ and }m\neq 4$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

n qiymati -9 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(m+1\right)\left(n+9\right) ga, n+9,m+1 ning eng kichik karralisiga ko‘paytiring.

$$\left(m+1\right)m=\left(n+9\right)\left(m-4\right)$$

m+1 ga m ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$m^{2}+m=\left(n+9\right)\left(m-4\right)$$

n+9 ga m-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$m^{2}+m=nm-4n+9m-36$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$nm-4n+9m-36=m^{2}+m$$

Ikkala tarafdan 9m ni ayirish.

$$nm-4n-36=m^{2}+m-9m$$

-8m ni olish uchun m va -9m ni birlashtirish.

$$nm-4n-36=m^{2}-8m$$

36 ni ikki tarafga qo’shing.

$$nm-4n=m^{2}-8m+36$$

n'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(m-4\right)n=m^{2}-8m+36$$

Ikki tarafini m-4 ga bo‘ling.

$$\frac{\left(m-4\right)n}{m-4}=\frac{m^{2}-8m+36}{m-4}$$

m-4 ga bo'lish m-4 ga ko'paytirishni bekor qiladi.

$$n=\frac{m^{2}-8m+36}{m-4}$$

n qiymati -9 teng bo‘lmaydi.

$$n=\frac{m^{2}-8m+36}{m-4}\text{, }n\neq -9$$

m uchun yechish

$$m=\frac{\sqrt{n^{2}-80}+n+8}{2}$$

$$m=\frac{-\sqrt{n^{2}-80}+n+8}{2}\text{, }n\geq 4\sqrt{5}\text{ or }\left(n\neq -9\text{ and }n\leq -4\sqrt{5}\right)$$