Question

Divide. (x²+8xy-20y²)/(x²-10xy+21y²)-:(x+10y)/(2x-14y).

Answer 1

To solve the division of algebraic fractions, multiply the first fraction by the reciprocal of the second. Factor and cancel common terms where possible.

Step-by-step explanation:

To divide the given algebraic fractions, we need to multiply the first fraction by the reciprocal of the second fraction. This process is also known as division of fractions or performing a division operation.

The original expression is
`(x²+8xy-20y²)/(x²-10xy+21y²) ÷ (x+10y)/(2x-14y)`.

We need to find the reciprocal of the second fraction and then multiply it with the first.

The reciprocal of
`(x+10y)/(2x-14y) is (2x-14y)/(x+10y)`.

Now we multiply the two fractions:

`(x²+8xy-20y²)/(x²-10xy+21y²) × (2x-14y)/(x+10y)`

The next step would be to factor the numerators and denominators when possible and then reduce the expression by canceling out common factors. However, without specific factors provided for these quadratics, we would be unable to simplify further without additional information. If you can factor the quadratics, proceed with cancellation where possible.