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ANTONII [103]
3 years ago
12

Can someone please help? Thank you!

Mathematics
1 answer:
Svetradugi [14.3K]3 years ago
8 0

Answer:

\dfrac{2x(5x+1)}{4x-1}

Step-by-step explanation:

Given expression:

\dfrac{\dfrac{4x^3-12x^2}{4x^2+7x-2}}{\dfrac{2x^2-6x}{5x^2+11x+2}}

Consider the numerator and the denominator separately.

Numerator:

\dfrac{4x^3-12x^2}{4x^2+7x-2}\\ \\=\dfrac{4x^2(x-3)}{4x^2+8x-x-2}\\ \\=\dfrac{4x^2(x-3)}{4x(x+2)-(x+2)}\\ \\=\dfrac{4x^2(x-3)}{(x+2)(4x-1)}

Denominator:

\dfrac{2x^2-6x}{5x^2+11x+2}\\ \\=\dfrac{2x(x-3)}{5x^2+10x+x+2}\\ \\=\dfrac{2x(x-3)}{5x(x+2)+(x+2)}\\ \\=\dfrac{2x(x-3)}{(x+2)(5x+1)}

The whole expression:

\dfrac{\dfrac{4x^3-12x^2}{4x^2+7x-2}}{\dfrac{2x^2-6x}{5x^2+11x+2}}\\ \\ \\=\dfrac{\dfrac{4x^2(x-3)}{(x+2)(4x-1)}}{\dfrac{2x(x-3)}{(x+2)(5x+1)}}\\ \\ \\=\dfrac{4x^2(x-3)}{(x+2)(4x-1)}\cdot \dfrac{(x+2)(5x+1)}{2x(x-3)}\\ \\ \\=\dfrac{2x(5x+1)}{4x-1}

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