1. divide and simplify x^2+x-56/x^1-1 / x-7/2x+2
2. find the product in simplest from for x^2+x-6/2x^2-x-3 * x^7-2x^6+4x^5/x^4+8x
3. perform the indicated operations and simplify: 2/3x +4/3x^2 y^4 -6/2x^4 y^5
4. perform the indicated operation and simplify x/x-1 + 2x+3/x^2-1
5. build the fraction 3+x/x^4 to an equivalent fraction whoes denominator is x^6
I guess if you knew how to use parentheses to tell us what is numerator and what is denominator and what is exponent of what you would not be asking the question so I do not know what to say.
to group some terms that is difficult to solve,then,when we group that terms they will be easy to solve.
7/6 divided 1/8 times 1/4
I don't know good luck dude
1. To divide and simplify the expression (x^2 + x - 56) / (x - 1) divided by (x - 7) / (2x + 2), you need to follow these steps:
Step 1: Factorize the numerator and denominator of each fraction.
The numerator, x^2 + x - 56, factors to (x + 8)(x - 7).
The denominator, x - 1, is already in factored form.
The numerator, x - 7, is already in factored form.
The denominator, 2x + 2, factors to 2(x + 1).
Step 2: Rewrite the expression as a multiplication problem.
(x + 8)(x - 7) / (x - 1) * 1 / [2(x + 1)] (Note: reciprocal of x - 7 and 2x + 2)
Step 3: Simplify the expression.
Cancel out common factors between the numerator and denominator.
(x + 8) / (x - 1) * 1 / 2
Simplify the expression further by distributing the factor of 1/2 to the numerator.
(x + 8) / 2(x - 1)
Final simplified expression: (x + 8) / 2x - 2
2. To find the product in simplest form for [(x^2 + x - 6) / (2x^2 - x - 3)] * [(x^7 - 2x^6 + 4x^5) / (x^4 + 8x)], follow these steps:
Step 1: Factorize the numerator and denominator.
The first fraction numerator, x^2 + x - 6, factors to (x + 3)(x - 2).
The first fraction denominator, 2x^2 - x - 3, factors to (2x + 3)(x - 1).
The second fraction numerator, x^7 - 2x^6 + 4x^5, is already in factored form.
The second fraction denominator, x^4 + 8x, factors to x(x^3 + 8).
Step 2: Rewrite the expression as a multiplication problem.
[(x + 3)(x - 2) / (2x + 3)(x - 1)] * [x^7 - 2x^6 + 4x^5 / x(x^3 + 8)] (Note: reciprocal of the denominator)
Step 3: Simplify the expression.
Cancel out common factors between the numerator and denominator.
(x + 3)(x - 2) / (2x + 3)(x - 1) * [x^6(x - 2) + 4x^4 / (x^3 + 8)]
Multiply the numerators and the denominators.
[(x + 3)(x - 2)(x^6(x - 2) + 4x^4)] / [(2x + 3)(x - 1)(x^3 + 8)]
Perform the necessary multiplications.
[(x + 3)(x - 2)(x^7 - 2x^6 + 4x^5)] / [(2x + 3)(x - 1)(x^3 + 8)]
This is the simplified form of the expression.
3. To perform the indicated operations and simplify the expression 2/(3x) + 4/(3x^2y^4) - 6/(2x^4y^5), follow these steps:
Step 1: Find the least common denominator (LCD) of the fractions, which is the lowest common multiple of the denominators.
The denominators are 3x, 3x^2y^4, and 2x^4y^5.
The LCD is 6x^4y^5.
Step 2: Rewrite the fractions with the LCD as the denominator.
2(2x^3y^4)/(2*3x^4y^5) + 4(2x^2)/(2*3*x^2y^4) - 6(3x^3y)/(3*2x^4y^5)
Step 3: Combine the numerators over the common denominator.
4x^3y^4/6x^4y^5 + 8x^2/6x^2y^4 - 9x^3y/6x^4y^5
Step 4: Simplify the expression further by canceling out common factors.
2x^3y^4/3x^4y^5 + 4/3y^4 - 3x/2x^4y^5
Step 5: Combine like terms and simplify.
(2x^3y^4 - 9x)/(3x^4y^5) + 4/3y^4
This is the simplified form of the expression.
4. To perform the indicated operation and simplify the expression (x / (x - 1)) + ((2x + 3) / (x^2 - 1)), follow these steps:
Step 1: Factorize the denominators.
The first term denominator, (x - 1), is already factored.
The second term denominator, x^2 - 1, factors to (x - 1)(x + 1).
Step 2: Rewrite the expression with a common denominator.
x / (x - 1) + (2x + 3) / [(x - 1)(x + 1)]
Step 3: Combine the fractions over the common denominator.
[x(x + 1)] / [(x - 1)(x + 1)] + (2x + 3) / [(x - 1)(x + 1)]
Step 4: Simplify the expression further.
[x(x + 1) + (2x + 3)] / [(x - 1)(x + 1)]
Step 5: Expand and combine like terms.
(x^2 + x + 2x + 3) / [(x - 1)(x + 1)]
Step 6: Simplify the expression by factoring the numerator.
(x^2 + 3x + 3) / [(x - 1)(x + 1)]
This is the simplified form of the expression.
5. To build the fraction (3 + x) / x^4 into an equivalent fraction with a denominator of x^6, follow these steps:
Step 1: Start with the given fraction.
(3 + x) / x^4
Step 2: Rewrite the fraction with the new denominator.
[(3 + x) * x^2] / x^4 * x^2
Step 3: Simplify the expression.
(x^3 + x^3) / x^6
Step 4: Combine like terms and simplify.
2x^3 / x^6
This is the equivalent fraction with a denominator of x^6.