Question

7 класс. 1) 2x/a-b - x/b-a. 2)x/2m-n + y/b-2m.

Answer 1

Ответ:

$\displaystyle \tt 1) \; \frac{2 \cdot x}{a-b}-\frac{x}{b-a}=\frac{3 \cdot x}{a-b};\\\\ 2) \; \frac{x}{2 \cdot m-n}+\frac{y}{n-2 \cdot m}=\frac{x-y}{2 \cdot m-n}.$

Объяснение:

Требуется упростить (условие исправлено):

$\displaystyle \tt 1) \; \frac{2 \cdot x}{a-b}-\frac{x}{b-a};\\\\ 2) \; \frac{x}{2 \cdot m-n}+\frac{y}{n-2 \cdot m}.$

Решение. Дроби приведём к общему знаменателю и упростим:

$\displaystyle \tt 1) \; \frac{2 \cdot x}{a-b}-\frac{x}{b-a}=\frac{2 \cdot x}{a-b}-\frac{x}{-(a-b)}=\frac{2 \cdot x}{a-b}+\frac{x}{a-b}=\frac{2 \cdot x+x}{a-b}=\frac{3 \cdot x}{a-b};\\\\ 2) \; \frac{x}{2 \cdot m-n}+\frac{y}{n-2 \cdot m}=\frac{x}{2 \cdot m-n}+\frac{y}{-(2 \cdot m-n)}=\frac{x}{2 \cdot m-n}-\frac{y}{2 \cdot m-n}=\\\\=\frac{x-y}{2 \cdot m-n}.$

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Answer 2

To simplify the given expressions, I'll assume that the variables x, y, a, b, m, and n are all real numbers and that the denominators are non-zero.

1. Simplifying the expression 2x/a - b - x/b - a:

Step 1: Find a common denominator for the fractions, which is (a * b):

(2x * b - bx) / (a * b)

Step 2: Combine like terms:

(2bx - bx) / (a * b)

Step 3: Simplify:

bx / (a * b)

The simplified expression is bx / (a * b).

2. Simplifying the expression x / (2m - n) + y / (b - 2m):

The denominators are (2m - n) and (b - 2m). We need to find a common denominator for the fractions, which is (2m - n)(b - 2m):

Step 1: Rewrite each fraction with the common denominator:

[(x * (b - 2m)) + (y * (2m - n))] / [(2m - n)(b - 2m)]

Step 2: Expand the terms in the numerator:

[xb - 2mx + 2my - ny] / [(2m - n)(b - 2m)]

The simplified expression is (xb - 2mx + 2my - ny) / [(2m - n)(b - 2m)].