Verified Answer :

Panoyin

\(\frac{6x + 9}{15x^{2}} \div \frac{16x - 12}{10x^{4}}\)
\(\frac{3(2x) + 3(3)}{3(5x^{2})} \div \frac{4(4x) - 4(3)}{2(5x^{4})}\)
\(\frac{3(2x + 3)}{3(5x^{2})} \div \frac{4(4x - 3)}{2(5x^{4})}\)
\(\frac{2x + 3}{5x^{2}} \div \frac{2(4x - 3)}{5x^{4}}\)
\(\frac{2x + 3}{5x^{2}} \times \frac{5x^{4}}{2(4x - 3)}\)
\(\frac{2x + 3}{1} \times \frac{x^{2}}{2(4x - 3)}\)
\(\frac{2x^{3} + 3x^{2}}{8x - 6}\)

Answer

Simplify the quantity 6 x plus 9 over 15 x squared all over quantity 16 x minus 12 over 10 x to the fourth power .

To prove

As given

the quantity 6 x plus 9 over 15 x squared all over quantity 16 x minus 12 over 10 x to the fourth power .

Now written this in the simple form

\(= \frac{\frac{6x+9}{15x^{2}}{\frac{16x -12}{10x^{4}}\)

Now simplify the above equation

\(= \frac{\frac{6x+9\times 10x^{4}}{15x^{2}\times 16x-12}\)

Now using the property

\(\frac{y^{a}}{y^{b}} = y^{a-b}\)

Thus

\(= \frac{\frac{6x+9\times 10x^{4 -2}}{15\times 16x-12}\)

\(= \frac{\frac{6x+9\times 10x^{2}}{15\times 16x-12}\)

Now again simplify the above equation

\(= \frac{3(2x+3)\times 10x^{2}}{15\times 4(4x-3)}\)

Thus

\(= \frac{(2x+3)\times x^{2}}{2\times (4x-3)}\)

Therefore

\(= \frac{2x^{3}+3x^{2}} {8x-6}\)

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