We read your photo as:

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

Mathematics

ScanSolve AI Answer

Step-by-step solution

26 steps

  1. Simplify the parentheses.

    1+1=21 + 1 = 2

  2. Substitute into the expression.

    62+22\frac{6}{2} + \frac{2}{2}

  3. Simplify the fractions.

    3+13 + 1

  4. Add the terms.

    44

    4

  5. Group like terms for aa and bb.

    (a−a)+(b−b)(a - a) + (b - b)

  6. Simplify each pair.

    0+00 + 0

  7. Result.

    00

    0

  8. Simplify the second fraction.

    615=25\frac{6}{15} = \frac{2}{5}

  9. Substitute.

    35−25\frac{3}{5} - \frac{2}{5}

  10. Subtract the fractions.

    15\frac{1}{5}

    \dfrac{1}{5}

  11. Expand the distributed term.

    5(a−b)=5a−5b5(a - b) = 5a - 5b

  12. Substitute into the expression.

    a+2−a+5a−5ba + 2 - a + 5a - 5b

  13. Group like terms.

    (a−a+5a)+2−5b=5a+2−5b(a - a + 5a) + 2 - 5b = 5a + 2 - 5b

    5a - 5b + 2

  14. Expand each parentheses.

    5(a+b)=5a+5b5(a + b) = 5a + 5b −3(a−b)=−3a+3b-3(a - b) = -3a + 3b

  15. Substitute.

    5a+5b−3a+3b5a + 5b - 3a + 3b

  16. Group like terms.

    (5a−3a)+(5b+3b)=2a+8b(5a - 3a) + (5b + 3b) = 2a + 8b

    2a + 8b

  17. Write all terms.

    x+32x+2x+34xx + \frac{3}{2}x + 2x + \frac{3}{4}x

  18. Factor out xx.

    x(1+32+2+34)x\left(1 + \frac{3}{2} + 2 + \frac{3}{4}\right)

  19. Simplify the coefficients (common denominator 4).

    1=44,32=64,2=84,34=341 = \frac{4}{4}, \quad \frac{3}{2} = \frac{6}{4}, \quad 2 = \frac{8}{4}, \quad \frac{3}{4} = \frac{3}{4} 4+6+8+34=214\frac{4 + 6 + 8 + 3}{4} = \frac{21}{4}

  20. Result.

    214x\frac{21}{4}x

    \dfrac{21}{4}x

  21. Multiply the coefficients and variables.

    3×5=153 \times 5 = 15 ab×c=abcab \times c = abc

  22. Combine.

    15abc15abc

    15abc

  23. Write the expression (combining like terms).

    5m−3m+2m5m - 3m + 2m

  24. Combine coefficients.

    (5−3+2)m=4m(5 - 3 + 2)m = 4m

    4m

  25. Combine like terms for kk.

    k+3k−5=4k−5k + 3k - 5 = 4k - 5

    4k - 5

  26. Group like terms.

    (3a+a)+(5b−3b)=4a+2b(3a + a) + (5b - 3b) = 4a + 2b

    4a + 2b

Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QSimplify the following algebraic fractions: 1) 3/5x2 - 3/2x, 2) 1/y2 - 3/2y − 1/3y, 3) 3/4t2 - 5/6t2…QSimplify the expression 4(3x − 2y) − 3(x + 5y).QSimplify these fractions: 1. (18)/(8) × (15)/(3) × (16)/(4) 2. (12)/(4) × (16)/(12) x (y)/(8)QSimplify the following: (3a+5b)/4 + (9+b)/8 (2x)/6 + (2x−3y)/3 + (x+y)/2 (2a+4b)/4 − 3(a−4b)/6…
Browse by topic:AlgebraPre-Algebra
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.