Simplify the following algebraic fractions: 3(5x-8y)/4 - 4(6x-15y)/5

Step 1: Simplify the parentheses.
$1 + 1 = 2$

Step 2: Substitute into the expression.
$\frac{6}{2} + \frac{2}{2}$

Step 3: Simplify the fractions.
$3 + 1$

Step 4: Add the terms.
$4$

4

Step 1: Group like terms for $a$ and $b$.
$(a - a) + (b - b)$

Step 2: Simplify each pair.
$0 + 0$

Step 3: Result.
$0$

0

Step 1: Simplify the second fraction.
$\frac{6}{15} = \frac{2}{5}$

Step 2: Substitute.
$\frac{3}{5} - \frac{2}{5}$

Step 3: Subtract the fractions.
$\frac{1}{5}$

\dfrac{1{5}}

Step 1: Expand the distributed term.
$5(a - b) = 5a - 5b$

Step 2: Substitute into the expression.
$a + 2 - a + 5a - 5b$

Step 3: Group like terms.
$(a - a + 5a) + 2 - 5b = 5a + 2 - 5b$

5a - 5b + 2

Step 1: Expand each parentheses.
$5(a + b) = 5a + 5b$
$-3(a - b) = -3a + 3b$

Step 2: Substitute.
$5a + 5b - 3a + 3b$

Step 3: Group like terms.
$(5a - 3a) + (5b + 3b) = 2a + 8b$

2a + 8b

Step 1: Write all terms.
$x + \frac{3}{2}x + 2x + \frac{3}{4}x$

Step 2: Factor out $x$.
$x\left(1 + \frac{3}{2} + 2 + \frac{3}{4}\right)$

Step 3: Simplify the coefficients (common denominator 4).
$1 = \frac{4}{4}, \quad \frac{3}{2} = \frac{6}{4}, \quad 2 = \frac{8}{4}, \quad \frac{3}{4} = \frac{3}{4}$
$\frac{4 + 6 + 8 + 3}{4} = \frac{21}{4}$

Step 4: Result.
$\frac{21}{4}x$

\dfrac{21{4}x}

Step 1: Multiply the coefficients and variables.
$3 \times 5 = 15$
$ab \times c = abc$

Step 2: Combine.
$15abc$

15abc

Step 1: Write the expression (combining like terms).
$5m - 3m + 2m$

Step 2: Combine coefficients.
$(5 - 3 + 2)m = 4m$

4m

Step 1: Combine like terms for $k$.
$k + 3k - 5 = 4k - 5$

4k - 5

Step 1: Group like terms.
$(3a + a) + (5b - 3b) = 4a + 2b$

4a + 2b