86. $$ \frac{10+7 x-12 x^{2}}{8 x^{2}-2 x-15} \div \frac{6 x^{2}-13 x+5}{10 x^{2}-13 x+4} $$

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Simplify the expression by following steps:
- step0: Solution:
  $$\frac{\frac{\left(10+7x-12x^{2}\right)\left(10x^{2}-13x+4\right)}{\left(8x^{2}-2x-15\right)}}{\left(6x^{2}-13x+5\right)}$$
- step1: Remove the parentheses:
  $$\frac{\frac{\left(10+7x-12x^{2}\right)\left(10x^{2}-13x+4\right)}{8x^{2}-2x-15}}{6x^{2}-13x+5}$$
- step2: Multiply by the reciprocal:
  $$\frac{\left(10+7x-12x^{2}\right)\left(10x^{2}-13x+4\right)}{8x^{2}-2x-15}\times \frac{1}{6x^{2}-13x+5}$$
- step3: Rewrite the expression:
  $$\frac{\left(10+7x-12x^{2}\right)\left(2x-1\right)\left(5x-4\right)}{8x^{2}-2x-15}\times \frac{1}{\left(2x-1\right)\left(3x-5\right)}$$
- step4: Reduce the fraction:
  $$\frac{\left(10+7x-12x^{2}\right)\left(5x-4\right)}{8x^{2}-2x-15}\times \frac{1}{3x-5}$$
- step5: Multiply the terms:
  $$\frac{\left(10+7x-12x^{2}\right)\left(5x-4\right)}{\left(8x^{2}-2x-15\right)\left(3x-5\right)}$$
- step6: Multiply the terms:
  $$\frac{22x-40+83x^{2}-60x^{3}}{24x^{3}-46x^{2}-35x+75}$$
Calculate or simplify the expression $$ (10 + 7*x - 12*x^2) / (8*x^2 - 2*x - 15) / ((6*x^2 - 13*x + 5) / (10*x^2 - 13*x + 4)) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{\frac{\left(10+7x-12x^{2}\right)}{\left(8x^{2}-2x-15\right)}}{\left(\frac{\left(6x^{2}-13x+5\right)}{\left(10x^{2}-13x+4\right)}\right)}$$
- step1: Remove the parentheses:
  $$\frac{\frac{10+7x-12x^{2}}{8x^{2}-2x-15}}{\frac{6x^{2}-13x+5}{10x^{2}-13x+4}}$$
- step2: Divide the terms:
  $$\frac{\frac{10+7x-12x^{2}}{8x^{2}-2x-15}}{\frac{3x-5}{5x-4}}$$
- step3: Multiply by the reciprocal:
  $$\frac{10+7x-12x^{2}}{8x^{2}-2x-15}\times \frac{5x-4}{3x-5}$$
- step4: Multiply the terms:
  $$\frac{\left(10+7x-12x^{2}\right)\left(5x-4\right)}{\left(8x^{2}-2x-15\right)\left(3x-5\right)}$$
- step5: Multiply the terms:
  $$\frac{22x-40+83x^{2}-60x^{3}}{24x^{3}-46x^{2}-35x+75}$$
To solve the expression

$$
\frac{10 + 7x - 12x^2}{8x^2 - 2x - 15} \div \frac{6x^2 - 13x + 5}{10x^2 - 13x + 4},
$$

we can rewrite the division as multiplication by the reciprocal:

$$
\frac{10 + 7x - 12x^2}{8x^2 - 2x - 15} \times \frac{10x^2 - 13x + 4}{6x^2 - 13x + 5}.
$$

Now, we can combine the fractions:

$$
\frac{(10 + 7x - 12x^2)(10x^2 - 13x + 4)}{(8x^2 - 2x - 15)(6x^2 - 13x + 5)}.
$$

After simplifying this expression, we find that the result is:

$$
\frac{22x - 40 + 83x^2 - 60x^3}{24x^3 - 46x^2 - 35x + 75}.
$$

Thus, the final simplified form of the original expression is:

$$
\frac{22x - 40 + 83x^2 - 60x^3}{24x^3 - 46x^2 - 35x + 75}.
$$
$$ \frac{22x - 40 + 83x^2 - 60x^3}{24x^3 - 46x^2 - 35x + 75} $$

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